fix(desktop): treat profile=default as this process's own home

_is_other_profile only allowed empty/current, so a ?profile=default
save skipped the session.info broadcast on the process whose config
it just wrote. Compare the resolved target to the process HERMES_HOME.

hermes_cli/web_server.py

@@ -7067,7 +7067,13 @@ async def update_config(body: ConfigUpdate, profile: Optional[str] = None):
 def _is_other_profile(profile: Optional[str]) -> bool:
     """True when ``profile`` names a profile other than this process's own."""
     requested = (profile or "").strip()
-    return bool(requested) and requested.lower() != "current"
+    if not requested or requested.lower() == "current":
+        return False
+    try:
+        target = _resolve_profile_dir(requested)
+    except HTTPException:
+        return True
+    return target.resolve() != get_process_hermes_home().resolve()
 
 
 def _approval_mode_of(config: Dict[str, Any]) -> str:

tests/hermes_cli/test_web_server_approvals_broadcast.py

@@ -99,6 +99,19 @@ class TestApprovalsSaveBroadcast:
             "re-emit session.info"
         )
 
+    def test_own_profile_named_default_broadcasts(self, client, broadcast_calls):
+        """Dashboard/desktop often send ?profile=default for this process's
+        own home. That is not an other-profile save and must still emit."""
+        resp = client.put(
+            "/api/config?profile=default",
+            json={"config": {"approvals": {"mode": "off"}}},
+        )
+        assert resp.status_code == 200
+        assert broadcast_calls, (
+            "?profile=default is this process's own HERMES_HOME; skipping "
+            "the broadcast leaves live sessions painting stale YOLO state"
+        )
+
     def test_other_profile_save_does_not_broadcast(self, client, broadcast_calls, monkeypatch, tmp_path):
         from hermes_cli import web_server