Fix active run elapsed restore

backend/api/server.py

@@ -1357,6 +1357,7 @@ def create_app(state: AgentState) -> FastAPI:
             started_event = {
                 'type': 'run_started',
                 'run_id': run_record.run_id,
+                'started_at': run_record.started_at,
                 'session_id': requested_session_id or '',
                 'account_id': request.account_id or '',
             }