perf: run post-completion memory/knowledge extraction in background

Move _extract_memories and _store_knowledge into a fire-and-forget
asyncio task so the "completed" WebSocket message reaches the frontend
immediately after the agent loop ends.

Made-with: Cursor

Author: wanming

backend/app/services/agent.py

@@ -489,8 +489,11 @@ async def run(
             self._stop_shake_detector()
 
         await self._notify_state_change(state)
-        await self._extract_memories(state, instruction)
-        await self._store_knowledge(state, instruction)
+
+        # Run post-completion work in background so the caller can send
+        # the "completed" message to the frontend immediately.
+        asyncio.create_task(self._post_completion(state, instruction))
+
         return state
 
     # ── Helpers ──────────────────────────────────────────────────────────
@@ -618,6 +621,11 @@ def _apply_stagnation_warning(self, state: AgentState, warning: str):
             "result": warning,
         })
 
+    async def _post_completion(self, state: AgentState, instruction: str):
+        """Background work after task ends (non-blocking)."""
+        await self._extract_memories(state, instruction)
+        await self._store_knowledge(state, instruction)
+
     async def _extract_memories(self, state: AgentState, instruction: str):
         """Extract and save memories on successful completion."""
         if state.status != TaskStatus.COMPLETED or not state.history: