## Why
Issue #23214 reports `/ps` showing no background terminals while the
status line still says it is waiting for a background terminal. The race
is in core: `write_stdin` can poll a process that exits before the
response returns. The process manager correctly returns `process_id:
None`, but the handler still emitted a `TerminalInteraction` event using
the requested session id, causing clients to believe a dead process was
still being polled.
Fixes#23214.
## What changed
- Suppress `TerminalInteraction` events for empty `write_stdin` polls
once `response.process_id` is `None`.
- Continue emitting interactions for non-empty stdin, even if that input
causes the process to exit before the response returns.
- Extend the unified exec integration test to assert completed empty
polls do not emit terminal interactions.
## Verification
- `cargo test -p codex-core --test all
unified_exec_emits_one_begin_and_one_end_event`
- `cargo test -p codex-core --test all
unified_exec_emits_terminal_interaction_for_write_stdin`
`cargo test -p codex-core` currently aborts in unrelated
`agent::control::tests::resume_agent_from_rollout_uses_edge_data_when_descendant_metadata_source_is_stale`
with a reproducible stack overflow.
e43a2e297f