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/lib.rs

@@ -15,9 +15,14 @@ mod realtime_prompt;
 mod responses_metadata;
 mod responses_retry;
 pub(crate) mod session;
+pub use codex_protocol::turn_input::NotSubmittedReason;
+pub use codex_protocol::turn_input::StartIfIdleSubmission;
+pub use codex_protocol::turn_input::SteerSubmission;
+pub use codex_protocol::turn_input::TurnInput;
+pub use codex_protocol::turn_input::TurnInputRequest;
+pub use codex_protocol::turn_input::TurnInputSubmission;
+pub use codex_protocol::turn_input::TurnStartOptions;
 pub use responses_metadata::CodexResponsesMetadata;
-pub use session::SteerInputError;
-pub use session::TurnInput;
 pub use turn_metadata::detached_memory_responses_metadata;
 mod codex_thread;
 mod compact_model_fallback;
@@ -25,16 +30,12 @@ mod compact_remote;
 mod compact_remote_history;
 mod compact_remote_v2;
 mod compact_token_budget;
-mod user_message_admission;
 pub use codex_thread::BackgroundTerminalInfo;
 pub use codex_thread::CodexThread;
 pub use codex_thread::CodexThreadSettingsOverrides;
 pub use codex_thread::ThreadConfigSnapshot;
-pub use codex_thread::TryStartTurnIfIdleError;
-pub use codex_thread::TryStartTurnIfIdleRejectionReason;
 pub use environment_config::EnvironmentConfig;
 pub use session::turn_context::TurnContext;
-pub use user_message_admission::UserMessageAdmission;
 mod agent;
 mod agent_communication;
 mod attestation;