feat(install-e2e): cover Setup.exe re-run as a windows update method

The last declared TODO: a user whose install is stale re-downloads
Hermes-Setup.exe and clicks Install over the existing install, the GUI
twin of re-running the one-liner. Windows shows the full installer UI on
a re-run (the already-installed fast path is macOS-only), so the existing
AHK install drive applies unchanged; install.ps1's repository stage
fetches the existing checkout forward to what main serves, now HEAD.

Invoke-PhaseInstallGui gains an update mode instead of a parallel copy:
the phase label, proof dir, and expected-sha assertion become parameters,
and the update-is-available assert stays install-only. The bootstrap log
rotates before the re-run so the AHK's completion fallback cannot match
the install phase's old completion line.

.github/workflows/install-e2e-windows-run.yml

@@ -92,12 +92,11 @@ jobs:
     #     Update button to click, no -IncludeDesktop to pass);
     #   * open-app-update needs an OS entry point, which only the
     #     desktop-bearing installs create.
-    # desktop-installer@latest as an UPDATE method is the one declared TODO.
     if: >-
       (inputs.install-method == 'installer-script'
         || (contains(fromJSON('["installer-script+desktop", "desktop-installer@latest"]'), inputs.install-method) && inputs.tag-has-desktop))
       && (contains(fromJSON('["hermes-update", "installer-script"]'), inputs.update-method)
-        || (contains(fromJSON('["installer-script+desktop", "hermes-desktop-app-update"]'), inputs.update-method) && inputs.tag-has-desktop)
+        || (contains(fromJSON('["installer-script+desktop", "hermes-desktop-app-update", "desktop-installer@latest"]'), inputs.update-method) && inputs.tag-has-desktop)
         || (inputs.update-method == 'open-app-update' && inputs.tag-has-desktop
             && contains(fromJSON('["desktop-installer@latest", "installer-script+desktop"]'), inputs.install-method)))
     runs-on: windows-latest