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/mcp-server/tests/suite/codex_tool.rs

@@ -564,7 +564,11 @@ async fn codex_tool_forwards_skills_extension_warnings() -> anyhow::Result<()> {
         warning_json["params"]["_meta"]["requestId"],
         codex_request_id
     );
-    assert_eq!(warning_json["params"]["id"], codex_request_id.to_string());
+    assert!(
+        warning_json["params"]["id"]
+            .as_str()
+            .is_some_and(|turn_id| !turn_id.is_empty())
+    );
     assert!(
         warning_json["params"]["_meta"]["threadId"]
             .as_str()