Add trace_id to TurnStartedEvent (#23980)

## Why
[Recent PR](https://github.com/openai/codex/pull/22709) removed
`trace_id` from `TurnContextItem`.

## What changed
- Add to `TurnStartedEvent` so rollout consumers can correlate turns
with telemetry traces.
- Note that the branch name is out of date because I originally re-added
to `TurnContextItem`, but we decided to move it to `TurnStartedEvent`.

## Verification
- `cargo test -p codex-protocol`
- `cargo test -p codex-core --lib
regular_turn_emits_turn_started_without_waiting_for_startup_prewarm`
- `cargo test -p codex-core --test all
emits_warning_when_resumed_model_differs`
- `cargo test -p codex-rollout`
- `cargo test -p codex-state`

codex-rs/app-server/src/bespoke_event_handling.rs

@@ -3219,6 +3219,7 @@ mod tests {
                 "turn-1",
                 &EventMsg::TurnStarted(codex_protocol::protocol::TurnStartedEvent {
                     turn_id: "turn-1".to_string(),
+                    trace_id: None,
                     started_at: Some(42),
                     model_context_window: None,
                     collaboration_mode_kind: Default::default(),
@@ -3252,6 +3253,7 @@ mod tests {
                 id: "turn-1".to_string(),
                 msg: EventMsg::TurnStarted(codex_protocol::protocol::TurnStartedEvent {
                     turn_id: "turn-1".to_string(),
+                    trace_id: None,
                     started_at: Some(42),
                     model_context_window: None,
                     collaboration_mode_kind: Default::default(),
@@ -3301,6 +3303,7 @@ mod tests {
                 &event_turn_id,
                 &EventMsg::TurnStarted(codex_protocol::protocol::TurnStartedEvent {
                     turn_id: event_turn_id.clone(),
+                    trace_id: None,
                     started_at: Some(42),
                     model_context_window: None,
                     collaboration_mode_kind: Default::default(),

codex-rs/app-server/src/request_processors/thread_processor_tests.rs

@@ -1155,6 +1155,7 @@ mod thread_processor_behavior_tests {
                 "turn-1",
                 &EventMsg::TurnStarted(codex_protocol::protocol::TurnStartedEvent {
                     turn_id: "turn-1".to_string(),
+                    trace_id: None,
                     started_at: None,
                     model_context_window: None,
                     collaboration_mode_kind: Default::default(),

codex-rs/app-server/tests/suite/v2/thread_resume.rs

@@ -1431,6 +1431,7 @@ async fn thread_resume_token_usage_replay_ignores_stale_interrupted_tail_turn()
             "type": "event_msg",
             "payload": serde_json::to_value(EventMsg::TurnStarted(TurnStartedEvent {
                 turn_id: stale_turn_id.to_string(),
+                trace_id: None,
                 started_at: None,
                 model_context_window: None,
                 collaboration_mode_kind: Default::default(),
@@ -1518,6 +1519,7 @@ async fn thread_resume_token_usage_replay_can_belong_to_interrupted_turn() -> Re
             "type": "event_msg",
             "payload": serde_json::to_value(EventMsg::TurnStarted(TurnStartedEvent {
                 turn_id: interrupted_turn_id.to_string(),
+                trace_id: None,
                 started_at: None,
                 model_context_window: None,
                 collaboration_mode_kind: Default::default(),
@@ -1835,6 +1837,7 @@ async fn thread_resume_and_read_interrupt_incomplete_rollout_turn_when_thread_is
             "type": "event_msg",
             "payload": serde_json::to_value(EventMsg::TurnStarted(TurnStartedEvent {
                 turn_id: turn_id.to_string(),
+                trace_id: None,
                 started_at: None,
                 model_context_window: None,
                 collaboration_mode_kind: Default::default(),