## What changed
- This PR changes only the flaky test setup for
`turn_start_notify_payload_includes_initialize_client_name`.
- Instead of shelling out to `python3` to write the notify payload, the
test uses the first-party `codex-app-server-test-notify-capture` helper.
- The helper writes `notify.json` atomically and the test waits for the
file to exist before reading it.
## Why this fixes the flake
- The old test depended on an external Python interpreter being present
and behaving consistently on every CI runner.
- It also raced the file write: the test could observe the path before
the payload had been fully written, which produced partial reads and
intermittent assertion failures.
- Moving the write into a repo-owned helper removes the external
dependency, and atomic write-plus-wait makes the handoff deterministic.
## Scope
- Test-only change.
- production logic plus tests; cancel running tasks before clearing
pending turn state
- suppress follow-up model requests after cancellation and assert on
stabilized request counts instead of fixed sleeps
