Fix live activity timer

backend/api/server.py

@@ -485,6 +485,7 @@ class RunManager:
                 'current_stage': record.current_stage,
                 'started_at': record.started_at,
                 'updated_at': record.updated_at,
+                'elapsed_ms': max(0, int((time.time() - record.started_at) * 1000)),
                 'pending_prompt': record.pending_prompt,
                 'error': record.error,
                 'events': [dict(event) for event in record.events],
@@ -1612,7 +1613,10 @@ def create_app(state: AgentState) -> FastAPI:
                 merged['events'] = stored_snapshot.get('events')
             if memory_snapshot.get('current_stage'):
                 merged['current_stage'] = memory_snapshot.get('current_stage')
-            if stored_snapshot.get('elapsed_ms') is not None:
+            if (
+                memory_snapshot.get('status') not in ACTIVE_RUN_STATUSES
+                and stored_snapshot.get('elapsed_ms') is not None
+            ):
                 merged['elapsed_ms'] = stored_snapshot.get('elapsed_ms')
             if stored_snapshot.get('finished_at') is not None:
                 merged['finished_at'] = stored_snapshot.get('finished_at')