fix(desktop): guard reconnect sockets and keep branch search precise

Avoid stale WebSocket events from an old reconnect attempt flipping the gateway state after a newer socket opens. Also limit session-search dedupe to compression edges so branch-specific hits still open the branch instead of collapsing to the parent.

tests/hermes_cli/test_web_server.py

@@ -466,6 +466,40 @@ class TestWebServerEndpoints:
         assert hit["session_id"] == "search-tip"
         assert hit["lineage_root"] == "search-root"
 
+    def test_search_keeps_branch_specific_hits_on_branch(self):
+        """Branch sessions share parent_session_id, but they are not compression
+        continuations. A query that only exists in the branch must open the
+        branch instead of being collapsed back to the parent/root."""
+        import time as _time
+
+        from hermes_state import SessionDB
+
+        db = SessionDB()
+        try:
+            now = _time.time()
+            db.create_session(session_id="branch-parent", source="cli")
+            db.append_message(session_id="branch-parent", role="user", content="ancestor context")
+            db.end_session("branch-parent", "branched")
+            db._conn.execute(
+                "UPDATE sessions SET started_at = ?, ended_at = ? WHERE id = ?",
+                (now - 100, now - 90, "branch-parent"),
+            )
+            db.create_session(session_id="branch-child", source="cli", parent_session_id="branch-parent")
+            db._conn.execute("UPDATE sessions SET started_at = ? WHERE id = ?", (now - 80, "branch-child"))
+            db.append_message(session_id="branch-child", role="user", content="branchspecificneedle only here")
+            db._conn.commit()
+        finally:
+            db.close()
+
+        resp = self.client.get("/api/sessions/search?q=branchspecificneedle")
+        assert resp.status_code == 200
+        results = resp.json()["results"]
+
+        assert any(
+            r["session_id"] == "branch-child" and r.get("lineage_root") == "branch-child"
+            for r in results
+        )
+
     def test_get_sessions_archived_is_boolean(self):
         from hermes_state import SessionDB