Fix stale background terminal poll events

[etraut-openai]

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.

[jif-oai]

This still seems racy for the adjacent ordering: if the process is alive when write_stdin builds the response but exits before this event is delivered, the exit watcher can clear the process first and then this empty interaction sets the stale “Waiting for background terminal” status again