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/tui/src/bottom_pane/request_user_input/mod.rs

@@ -1561,7 +1561,7 @@ mod tests {
         let AppEvent::CodexOp(op) = event else {
             panic!("expected CodexOp");
         };
-        assert_eq!(op, Op::interrupt());
+        assert!(matches!(op, Op::Interrupt));
         assert!(
             rx.try_recv().is_err(),
             "unexpected AppEvents before interrupt completion"