## Why
`cargo nextest` was intermittently reporting `LEAK` for
`codex-app-server` tests even when assertions passed. This adds noise
and flakiness to local/CI signals.
Sample output used as the basis of this investigation:
```text
LEAK [ 7.578s] ( 149/3663) codex-app-server::all suite::output_schema::send_user_turn_output_schema_is_per_turn_v1
LEAK [ 7.383s] ( 210/3663) codex-app-server::all suite::v2::dynamic_tools::dynamic_tool_call_round_trip_sends_text_content_items_to_model
LEAK [ 7.768s] ( 213/3663) codex-app-server::all suite::v2::dynamic_tools::thread_start_injects_dynamic_tools_into_model_requests
LEAK [ 8.841s] ( 224/3663) codex-app-server::all suite::v2::output_schema::turn_start_accepts_output_schema_v2
LEAK [ 8.151s] ( 225/3663) codex-app-server::all suite::v2::plan_item::plan_mode_uses_proposed_plan_block_for_plan_item
LEAK [ 8.230s] ( 232/3663) codex-app-server::all suite::v2::safety_check_downgrade::openai_model_header_mismatch_emits_model_rerouted_notification_v2
LEAK [ 6.472s] ( 273/3663) codex-app-server::all suite::v2::turn_start::turn_start_accepts_collaboration_mode_override_v2
LEAK [ 6.107s] ( 275/3663) codex-app-server::all suite::v2::turn_start::turn_start_accepts_personality_override_v2
```
## How I Reproduced
I focused on the suspect tests and ran them under `nextest` stress mode
with leak reporting enabled.
```bash
cargo nextest run -p codex-app-server -j 2 --no-fail-fast --stress-count 25 --status-level leak --final-status-level fail -E 'test(suite::output_schema::send_user_turn_output_schema_is_per_turn_v1) | test(suite::v2::dynamic_tools::dynamic_tool_call_round_trip_sends_text_content_items_to_model) | test(suite::v2::dynamic_tools::thread_start_injects_dynamic_tools_into_model_requests) | test(suite::v2::output_schema::turn_start_accepts_output_schema_v2) | test(suite::v2::plan_item::plan_mode_uses_proposed_plan_block_for_plan_item) | test(suite::v2::safety_check_downgrade::openai_model_header_mismatch_emits_model_rerouted_notification_v2) | test(suite::v2::turn_start::turn_start_accepts_collaboration_mode_override_v2) | test(suite::v2::turn_start::turn_start_accepts_personality_override_v2)'
```
This reproduced intermittent `LEAK` statuses while tests still passed.
## What Changed
In `codex-rs/app-server/tests/common/mcp_process.rs`:
- Changed `stdin: ChildStdin` to `stdin: Option<ChildStdin>` so teardown
can explicitly close stdin.
- In `Drop`, close stdin first to trigger EOF-based graceful shutdown.
- Wait briefly for graceful exit.
- If still running, fall back to `start_kill()` and the existing bounded
`try_wait()` loop.
- Updated send-path handling to bail if stdin is already closed.
## Why This Is the Right Fix
The leak signal was caused by child-process teardown timing, not
test-logic assertion failure. The helper previously relied mostly on
force-kill timing in `Drop`; that can race with nextest leak detection.
Closing stdin first gives `codex-app-server` a deterministic, graceful
shutdown path before force-kill. Keeping the force-kill fallback
preserves robustness if graceful shutdown does not complete in time.
## Verification
- `cargo test -p codex-app-server`
- Re-ran the stress repro above after this change: no `LEAK` statuses
observed.
- Additional high-signal stress run also showed no leaks:
```bash
cargo nextest run -p codex-app-server -j 2 --no-fail-fast --stress-count 100 --status-level leak --final-status-level fail -E 'test(suite::output_schema::send_user_turn_output_schema_is_per_turn_v1) | test(suite::v2::dynamic_tools::dynamic_tool_call_round_trip_sends_text_content_items_to_model)'
```
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