Unify turn input submission and routing (#38275)

## What changed

- Add `TurnInputRequest` and typed submission results for atomically starting a turn, steering the active turn, or declining input with a specific reason.
- Expose `start_or_steer_turn`, `start_turn_if_idle`, and `steer_turn` on `CodexThread`, and migrate Core consumers to these APIs.
- Make app-server `turn/start` steer an active regular turn and return that turn's ID. Reject incompatible output schemas and non-steerable turns without applying settings or enqueueing input.

## Testing

- Cover concurrent start-or-steer submissions, accepted and rejected settings updates, output-schema compatibility, idle-start rejection, and app-server steering.

GitOrigin-RevId: dd9b5528d76ec650c019e97af420bc13190ea86a

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

@@ -57,8 +57,6 @@ pub(crate) struct Session {
     pub(crate) conversation: Arc<RealtimeConversationManager>,
     pub(crate) active_turn: Mutex<Option<ActiveTurn>>,
     pub(crate) async_hook_results: async_channel::Receiver<HookCompletedEvent>,
-    pub(crate) pending_user_message_admissions:
-        crate::user_message_admission::PendingUserMessageAdmissions,
     pub(crate) input_queue: InputQueue,
     pub(crate) guardian_review_session: GuardianReviewSessionManager,
     pub(crate) services: SessionServices,
@@ -1312,7 +1310,6 @@ impl Session {
                 conversation: Arc::new(RealtimeConversationManager::new()),
                 active_turn: Mutex::new(None),
                 async_hook_results,
-                pending_user_message_admissions: Default::default(),
                 input_queue: InputQueue::new(),
                 guardian_review_session: GuardianReviewSessionManager::default(),
                 services,