Python: Background completion waiter can finalize a newer continuation under the same task ID #9441

Describe the bug

background_agents_wait_for_first_completion can finalize a different execution from the one it waited for when another caller continues the same background task before the waiter resumes.

The tool records (task_id, asyncio.Task) pairs before calling asyncio.wait(). After the wait completes, it finds the completed ID using those original task objects, but fetches the task to finalize again from runtime.in_flight_tasks[task_id]. The continuation tool reuses that ID and replaces its runtime task.

Consequently:

1. A waiter starts waiting for execution A of task 1.
2. Execution A finishes.
3. Another caller retrieves A's result and continues task 1, starting execution B.
4. The waiter resumes, recognizes A as completed, then tries to finalize B.

If B is still running, Task.exception() raises asyncio.InvalidStateError: Exception is not set. The wait tool fails even though the execution it waited for completed successfully.

Expected behavior

A wait operation should report the outcome of the execution it actually observed. A stale waiter must not consume or remove a newer execution registered under the same task ID.

Reproduction and evidence

I reproduced this on current main, commit 9a1d66b3e973bdbfdcd4359d72c5f6fd4ff4d931, with Python 3.13.15 on macOS.

The deterministic regression uses the provider's public start, wait, get-results, and continue tools with an offline child agent. Events pause the waiter after the real asyncio.wait() returns, allowing the result retrieval and continuation to run before the waiter processes its completed set. No runtime task or persisted state is replaced directly by the test.

The regression currently fails through:

background_agents_wait_for_first_completion
  -> _finalize_task(task_info, completed_task, runtime)
  -> completed_task.exception()
asyncio.exceptions.InvalidStateError: Exception is not set.

Proposed scoped fix

Finalize the exact task object returned in the original wait set, and only update/remove runtime state if it still refers to that same execution. Add coverage for a pending and a completed continuation, ordinary waits, and concurrent waiters.

This concerns the local wait/continuation race. It is separate from completed-task retention in #9387, distributed runtime ownership in #8760/#9040, and the release-timeout issue in #9231.