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/codex_delegate_tests.rs

@@ -128,7 +128,6 @@ async fn forward_ops_preserves_submission_trace_context() {
     let submission = Submission {
         id: "sub-1".to_string(),
         op: Op::Interrupt,
-        client_user_message_id: None,
         trace: Some(codex_protocol::protocol::W3cTraceContext {
             traceparent: Some(
                 "00-1234567890abcdef1234567890abcdef-1234567890abcdef-01".to_string(),