[codex-analytics] add protocol-native turn timestamps (#16638)

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[//]: # (BEGIN SAPLING FOOTER)
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with [ReviewStack](https://reviewstack.dev/openai/codex/pull/16638).
* #16870
* #16706
* #16659
* #16641
* #16640
* __->__ #16638

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

@@ -492,6 +492,7 @@ 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(),
+                started_at: None,
                 model_context_window: None,
                 collaboration_mode_kind: Default::default(),
             }))?,