Background task results may be lost when agent loop exits early

[QianzhenSun]

In s08_background_tasks.py, background task results are delivered via a pull-based notification queue that is only drained before each LLM
call. However, if the LLM decides it has no more work to do (i.e., stop_reason != "tool_use"), the agent loop exits immediately, and any
pending background task results remain in the queue and are never delivered.

Steps to Reproduce

1. Ask the agent to run a long-running command in background:
   User: "Run npm test in the background"
2. Agent calls background_run("npm test") and receives a task_id
3. Agent responds with something like "OK, the test is running in the background"
4. LLM returns with stop_reason = "end_turn" (no tool calls)
5. Agent loop exits
6. Background task completes and enqueues result to _notification_queue
7. Result is never delivered since the loop has already exited