Accept user input when starting idle turns (#36947)

## What changed

- Generalize `CodexThread::try_start_turn_if_idle` to accept exported
  `TurnInput` values, preserving user content and client IDs in the first model
  request.
- Allow non-empty user input to start an idle turn in Plan mode while retaining
  the Plan-mode rejection for automatic response items and empty user input.
- Process idle user input through the normal user-turn path so connector
  selections are cleared, prompt telemetry is recorded, and referenced skill
  instructions are included.

## Testing

- Cover idle user input in Default and Plan modes, response-item mailbox
  merging, empty-input rejection, and skill instruction injection.

GitOrigin-RevId: 116667d160d4464b525d9e4c7e8cc05d23a94008

codex-rs/core/src/session/mod.rs

@@ -228,7 +228,7 @@ use self::config_lock::validate_config_lock_if_configured;
 use self::handlers::submission_dispatch_span;
 use self::handlers::submission_loop;
 pub(crate) use self::input_queue::InputQueueActivity;
-pub(crate) use self::input_queue::TurnInput;
+pub use self::input_queue::TurnInput;
 pub(crate) use self::input_queue::TurnInputQueue;
 use self::review::spawn_review_thread;
 use self::session::AppServerClientMetadata;