diff --git a/.github/workflows/install-e2e-macos-run.yml b/.github/workflows/install-e2e-macos-run.yml
index e23dcab79e..450cf42bc0 100644
--- a/.github/workflows/install-e2e-macos-run.yml
+++ b/.github/workflows/install-e2e-macos-run.yml
@@ -39,7 +39,7 @@ jobs:
     # Static name on purpose: the caller's job name already carries the
     # method pair, and GitHub renders name expressions UNEXPANDED (literal
     # "${{ inputs... }}") on natively skipped jobs.
-    name: run
+    name: e2e
     # No macOS driver exists yet: every pair is a declared TODO, so this is
     # constant-false until the first method lands. Written as an impossible
     # input comparison rather than `if: false` because actionlint rejects
diff --git a/.github/workflows/install-e2e-run.yml b/.github/workflows/install-e2e-run.yml
index 1d73af329e..c7077870ca 100644
--- a/.github/workflows/install-e2e-run.yml
+++ b/.github/workflows/install-e2e-run.yml
@@ -60,11 +60,11 @@ jobs:
   e2e:
     # Static name on purpose: the caller's job name already carries the
     # method pair, and GitHub renders name expressions UNEXPANDED (literal
-    # "${{ inputs... }}") on natively skipped jobs.
-    name: run
-    # The pairs the sandbox driver can run today. Anything else is a
-    # declared TODO: native skip, so the coverage gap is a grey check on
-    # every run.
+    # "${{ inputs... }}") on natively skipped jobs. Short because it is
+    # only a rendered tail ("<tag> -> HEAD / e2e").
+    name: e2e
+    # The pairs the sandbox driver can run today; anything else is a
+    # declared TODO and natively skips.
     if: inputs.install-method == 'curl-bash' && contains(fromJSON('["hermes-update", "curl-bash"]'), inputs.update-method)
     runs-on: ${{ inputs.runner }}
     timeout-minutes: ${{ inputs.timeout-minutes }}
diff --git a/.github/workflows/install-e2e-windows-run.yml b/.github/workflows/install-e2e-windows-run.yml
index c1e9a63ffd..fdac6d6ce0 100644
--- a/.github/workflows/install-e2e-windows-run.yml
+++ b/.github/workflows/install-e2e-windows-run.yml
@@ -57,6 +57,11 @@ on:
         required: false
         type: string
         default: auto
+      tag-has-desktop:
+        description: 'Whether install-ref ships the desktop app (apps/desktop). The caller annotates this from the tag''s own tree; desktop-method legs from pre-desktop releases natively skip.'
+        required: false
+        type: boolean
+        default: true
       setup-exe-url:
         description: 'Bootstrap installer to install OLD with. Default: the latest published one — what a user downloads today.'
         required: false
@@ -72,52 +77,17 @@ permissions:
   contents: read
 
 jobs:
-  # Can this starting version run this flow at all? The desktop app
-  # (apps/desktop) only exists in releases from v2026.5.31 on (#20059):
-  # older tags have no window to launch and no Update button to click, so
-  # desktop-method legs from them natively skip below. Data-driven from the
-  # tag's own tree -- no hardcoded version list to rot.
-  probe:
-    name: probe tag
-    if: inputs.install-method == 'desktop-installer@latest' && inputs.update-method == 'desktop-app'
-    runs-on: ubuntu-latest
-    timeout-minutes: 5
-    outputs:
-      has-desktop: ${{ steps.probe.outputs.has-desktop }}
-    steps:
-      # Tree listings only: no blobs, full history + tags so any ref
-      # resolves.
-      - uses: actions/checkout@de0fac2e4500dabe0009e67214ff5f5447ce83dd # v6.0.2
-        with:
-          fetch-depth: 0
-          filter: blob:none
-      - id: probe
-        run: |
-          set -euo pipefail
-          ref='${{ inputs.install-ref }}'
-          if [ "$ref" = "auto" ]; then
-            # Same choice the driver's stage phase makes: newest release tag.
-            ref="$(git tag --list 'v[0-9]*' --sort=-creatordate | head -1)"
-          fi
-          if git ls-tree -d "$ref" apps/desktop | grep -q .; then
-            has=true
-          else
-            has=false
-          fi
-          echo "ref $ref: has-desktop=$has"
-          echo "has-desktop=$has" >> "$GITHUB_OUTPUT"
-
   e2e:
     # Static name on purpose: the caller's job name already carries the
     # method pair, and GitHub renders name expressions UNEXPANDED (literal
     # "${{ inputs... }}") on natively skipped jobs.
-    name: run
-    needs: probe
+    name: e2e
     # The one pair the driver can run today, and only from a starting
-    # version that ships the desktop app. Anything else is a native skip:
-    # a declared-TODO method pair, or a tag from before the app existed.
-    # (When probe itself skipped, its output is empty and this is false.)
-    if: inputs.install-method == 'desktop-installer@latest' && inputs.update-method == 'desktop-app' && needs.probe.outputs.has-desktop == 'true'
+    # version that ships the desktop app (the caller annotates
+    # tag-has-desktop from the tag's own tree; releases before #20059 have
+    # no window to launch and no Update button to click). Anything else is
+    # a native skip: a declared-TODO method pair, or a pre-desktop tag.
+    if: inputs.install-method == 'desktop-installer@latest' && inputs.update-method == 'desktop-app' && inputs.tag-has-desktop
     runs-on: windows-latest
     timeout-minutes: ${{ inputs.timeout-minutes }}
 
diff --git a/.github/workflows/install-e2e.yml b/.github/workflows/install-e2e.yml
index c571186805..2a92db7578 100644
--- a/.github/workflows/install-e2e.yml
+++ b/.github/workflows/install-e2e.yml
@@ -95,12 +95,22 @@ jobs:
           set -euo pipefail
           tags="$(scripts/sandbox/pick-release-tags.sh --count '${{ inputs.tag-count || 5 }}')"
           echo "Testing updates from: $tags"
-          echo "tags=$tags" >> "$GITHUB_OUTPUT"
+          # Annotate each tag with what its own tree supports, so legs can
+          # natively skip surfaces the starting version does not have.
+          # Today: does the release ship the desktop app (apps/desktop,
+          # #20059)? Cheaper and simpler here -- the tags are already
+          # checked out -- than a probe job per windows leg.
+          enriched="$(for t in $(echo "$tags" | jq -r '.[]'); do
+            if git ls-tree -d "$t" apps/desktop | grep -q .; then d=true; else d=false; fi
+            echo "{\"ref\":\"$t\",\"desktop\":$d}"
+          done | jq -sc .)"
+          echo "Annotated: $enriched"
+          echo "tags=$enriched" >> "$GITHUB_OUTPUT"
 
   # ---- linux: install via curl-bash ---------------------------------------
 
   linux-curl-bash-to-hermes-update:
-    name: "linux: curl-bash -> hermes-update"
+    name: "${{ matrix.tag.ref }} -> HEAD"
     if: github.event_name != 'workflow_dispatch' || contains(fromJSON('["all", "both", "update"]'), inputs.route)
     needs: pick-releases
     strategy:
@@ -108,32 +118,32 @@ jobs:
       # failed, so let every leg report.
       fail-fast: false
       matrix:
-        install-ref: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
+        tag: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
     uses: ./.github/workflows/install-e2e-run.yml
     with:
       install-method: curl-bash
       update-method: hermes-update
-      install-ref: ${{ matrix.install-ref }}
+      install-ref: ${{ matrix.tag.ref }}
 
   linux-curl-bash-to-curl-bash:
-    name: "linux: curl-bash -> curl-bash"
+    name: "${{ matrix.tag.ref }} -> HEAD"
     if: github.event_name != 'workflow_dispatch' || contains(fromJSON('["all", "both", "installer"]'), inputs.route)
     needs: pick-releases
     strategy:
       fail-fast: false
       max-parallel: 3
       matrix:
-        install-ref: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
+        tag: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
     uses: ./.github/workflows/install-e2e-run.yml
     with:
       install-method: curl-bash
       update-method: curl-bash
-      install-ref: ${{ matrix.install-ref }}
+      install-ref: ${{ matrix.tag.ref }}
 
   # ---- windows: install via the website's Hermes-Setup.exe ----------------
 
   windows-desktop-installer-to-desktop-app:
-    name: "windows: desktop-installer@latest -> desktop-app"
+    name: "${{ matrix.tag.ref }} -> HEAD"
     if: github.event_name != 'workflow_dispatch' || contains(fromJSON('["all", "windows-desktop"]'), inputs.route)
     needs: pick-releases
     strategy:
@@ -142,195 +152,203 @@ jobs:
       # enough for a 5-tag axis without hogging the Windows pool.
       max-parallel: 2
       matrix:
-        install-ref: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
+        tag: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
     uses: ./.github/workflows/install-e2e-windows-run.yml
     with:
+      tag-has-desktop: ${{ matrix.tag.desktop }}
       install-method: desktop-installer@latest
       update-method: desktop-app
-      install-ref: ${{ matrix.install-ref }}
+      install-ref: ${{ matrix.tag.ref }}
 
   windows-desktop-installer-to-installer-rerun:
-    name: "windows: desktop-installer@latest -> desktop-installer-rerun@latest"
+    name: "${{ matrix.tag.ref }} -> HEAD"
     if: github.event_name != 'workflow_dispatch' || contains(fromJSON('["all", "windows-desktop"]'), inputs.route)
     needs: pick-releases
     strategy:
       fail-fast: false
       matrix:
-        install-ref: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
+        tag: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
     uses: ./.github/workflows/install-e2e-windows-run.yml
     with:
+      tag-has-desktop: ${{ matrix.tag.desktop }}
       install-method: desktop-installer@latest
       update-method: desktop-installer-rerun@latest
-      install-ref: ${{ matrix.install-ref }}
+      install-ref: ${{ matrix.tag.ref }}
 
   windows-desktop-installer-to-hermes-update:
-    name: "windows: desktop-installer@latest -> hermes-update"
+    name: "${{ matrix.tag.ref }} -> HEAD"
     if: github.event_name != 'workflow_dispatch' || contains(fromJSON('["all", "windows-desktop"]'), inputs.route)
     needs: pick-releases
     strategy:
       fail-fast: false
       matrix:
-        install-ref: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
+        tag: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
     uses: ./.github/workflows/install-e2e-windows-run.yml
     with:
+      tag-has-desktop: ${{ matrix.tag.desktop }}
       install-method: desktop-installer@latest
       update-method: hermes-update
-      install-ref: ${{ matrix.install-ref }}
+      install-ref: ${{ matrix.tag.ref }}
 
   windows-desktop-installer-to-irm-iex:
-    name: "windows: desktop-installer@latest -> irm-iex"
+    name: "${{ matrix.tag.ref }} -> HEAD"
     if: github.event_name != 'workflow_dispatch' || contains(fromJSON('["all", "windows-desktop"]'), inputs.route)
     needs: pick-releases
     strategy:
       fail-fast: false
       matrix:
-        install-ref: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
+        tag: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
     uses: ./.github/workflows/install-e2e-windows-run.yml
     with:
+      tag-has-desktop: ${{ matrix.tag.desktop }}
       install-method: desktop-installer@latest
       update-method: irm-iex
-      install-ref: ${{ matrix.install-ref }}
+      install-ref: ${{ matrix.tag.ref }}
 
   # ---- windows: install via irm | iex --------------------------------------
 
   windows-irm-iex-to-desktop-app:
-    name: "windows: irm-iex -> desktop-app"
+    name: "${{ matrix.tag.ref }} -> HEAD"
     if: github.event_name != 'workflow_dispatch' || contains(fromJSON('["all", "windows-desktop"]'), inputs.route)
     needs: pick-releases
     strategy:
       fail-fast: false
       matrix:
-        install-ref: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
+        tag: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
     uses: ./.github/workflows/install-e2e-windows-run.yml
     with:
+      tag-has-desktop: ${{ matrix.tag.desktop }}
       install-method: irm-iex
       update-method: desktop-app
-      install-ref: ${{ matrix.install-ref }}
+      install-ref: ${{ matrix.tag.ref }}
 
   windows-irm-iex-to-installer-rerun:
-    name: "windows: irm-iex -> desktop-installer-rerun@latest"
+    name: "${{ matrix.tag.ref }} -> HEAD"
     if: github.event_name != 'workflow_dispatch' || contains(fromJSON('["all", "windows-desktop"]'), inputs.route)
     needs: pick-releases
     strategy:
       fail-fast: false
       matrix:
-        install-ref: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
+        tag: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
     uses: ./.github/workflows/install-e2e-windows-run.yml
     with:
+      tag-has-desktop: ${{ matrix.tag.desktop }}
       install-method: irm-iex
       update-method: desktop-installer-rerun@latest
-      install-ref: ${{ matrix.install-ref }}
+      install-ref: ${{ matrix.tag.ref }}
 
   windows-irm-iex-to-hermes-update:
-    name: "windows: irm-iex -> hermes-update"
+    name: "${{ matrix.tag.ref }} -> HEAD"
     if: github.event_name != 'workflow_dispatch' || contains(fromJSON('["all", "windows-desktop"]'), inputs.route)
     needs: pick-releases
     strategy:
       fail-fast: false
       matrix:
-        install-ref: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
+        tag: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
     uses: ./.github/workflows/install-e2e-windows-run.yml
     with:
+      tag-has-desktop: ${{ matrix.tag.desktop }}
       install-method: irm-iex
       update-method: hermes-update
-      install-ref: ${{ matrix.install-ref }}
+      install-ref: ${{ matrix.tag.ref }}
 
   windows-irm-iex-to-irm-iex:
-    name: "windows: irm-iex -> irm-iex"
+    name: "${{ matrix.tag.ref }} -> HEAD"
     if: github.event_name != 'workflow_dispatch' || contains(fromJSON('["all", "windows-desktop"]'), inputs.route)
     needs: pick-releases
     strategy:
       fail-fast: false
       matrix:
-        install-ref: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
+        tag: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
     uses: ./.github/workflows/install-e2e-windows-run.yml
     with:
+      tag-has-desktop: ${{ matrix.tag.desktop }}
       install-method: irm-iex
       update-method: irm-iex
-      install-ref: ${{ matrix.install-ref }}
+      install-ref: ${{ matrix.tag.ref }}
 
   # ---- macos: no driver yet (every leg natively skips in the run workflow) -
 
   macos-curl-bash-to-curl-bash:
-    name: "macos: curl-bash -> curl-bash"
+    name: "${{ matrix.tag.ref }} -> HEAD"
     if: github.event_name != 'workflow_dispatch' || inputs.route == 'all'
     needs: pick-releases
     strategy:
       fail-fast: false
       matrix:
-        install-ref: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
+        tag: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
     uses: ./.github/workflows/install-e2e-macos-run.yml
     with:
       install-method: curl-bash
       update-method: curl-bash
-      install-ref: ${{ matrix.install-ref }}
+      install-ref: ${{ matrix.tag.ref }}
 
   macos-curl-bash-to-hermes-update:
-    name: "macos: curl-bash -> hermes-update"
+    name: "${{ matrix.tag.ref }} -> HEAD"
     if: github.event_name != 'workflow_dispatch' || inputs.route == 'all'
     needs: pick-releases
     strategy:
       fail-fast: false
       matrix:
-        install-ref: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
+        tag: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
     uses: ./.github/workflows/install-e2e-macos-run.yml
     with:
       install-method: curl-bash
       update-method: hermes-update
-      install-ref: ${{ matrix.install-ref }}
+      install-ref: ${{ matrix.tag.ref }}
 
   macos-curl-bash-to-app-update:
-    name: "macos: curl-bash -> app-update"
+    name: "${{ matrix.tag.ref }} -> HEAD"
     if: github.event_name != 'workflow_dispatch' || inputs.route == 'all'
     needs: pick-releases
     strategy:
       fail-fast: false
       matrix:
-        install-ref: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
+        tag: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
     uses: ./.github/workflows/install-e2e-macos-run.yml
     with:
       install-method: curl-bash
       update-method: app-update
-      install-ref: ${{ matrix.install-ref }}
+      install-ref: ${{ matrix.tag.ref }}
 
   macos-packaged-app-to-curl-bash:
-    name: "macos: packaged-app -> curl-bash"
+    name: "${{ matrix.tag.ref }} -> HEAD"
     if: github.event_name != 'workflow_dispatch' || inputs.route == 'all'
     needs: pick-releases
     strategy:
       fail-fast: false
       matrix:
-        install-ref: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
+        tag: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
     uses: ./.github/workflows/install-e2e-macos-run.yml
     with:
       install-method: packaged-app
       update-method: curl-bash
-      install-ref: ${{ matrix.install-ref }}
+      install-ref: ${{ matrix.tag.ref }}
 
   macos-packaged-app-to-hermes-update:
-    name: "macos: packaged-app -> hermes-update"
+    name: "${{ matrix.tag.ref }} -> HEAD"
     if: github.event_name != 'workflow_dispatch' || inputs.route == 'all'
     needs: pick-releases
     strategy:
       fail-fast: false
       matrix:
-        install-ref: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
+        tag: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
     uses: ./.github/workflows/install-e2e-macos-run.yml
     with:
       install-method: packaged-app
       update-method: hermes-update
-      install-ref: ${{ matrix.install-ref }}
+      install-ref: ${{ matrix.tag.ref }}
 
   macos-packaged-app-to-app-update:
-    name: "macos: packaged-app -> app-update"
+    name: "${{ matrix.tag.ref }} -> HEAD"
     if: github.event_name != 'workflow_dispatch' || inputs.route == 'all'
     needs: pick-releases
     strategy:
       fail-fast: false
       matrix:
-        install-ref: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
+        tag: ${{ fromJSON(needs.pick-releases.outputs.tags) }}
     uses: ./.github/workflows/install-e2e-macos-run.yml
     with:
       install-method: packaged-app
       update-method: app-update
-      install-ref: ${{ matrix.install-ref }}
+      install-ref: ${{ matrix.tag.ref }}