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

---
[//]: # (BEGIN SAPLING FOOTER)
Stack created with [Sapling](https://sapling-scm.com). Best reviewed
with [ReviewStack](https://reviewstack.dev/openai/codex/pull/16638).
* #16870
* #16706
* #16659
* #16641
* #16640
* __->__ #16638

codex-rs/core/src/tasks/mod.rs

@@ -511,9 +511,15 @@ impl Session {
                 &[("token_type", "reasoning_output"), tmp_mem],
             );
         }
+        let (completed_at, duration_ms) = turn_context
+            .turn_timing_state
+            .completed_at_and_duration_ms()
+            .await;
         let event = EventMsg::TurnComplete(TurnCompleteEvent {
             turn_id: turn_context.sub_id.clone(),
             last_agent_message,
+            completed_at,
+            duration_ms,
         });
         self.send_event(turn_context.as_ref(), event).await;
 
@@ -588,9 +594,16 @@ impl Session {
             self.flush_rollout().await;
         }
 
+        let (completed_at, duration_ms) = task
+            .turn_context
+            .turn_timing_state
+            .completed_at_and_duration_ms()
+            .await;
         let event = EventMsg::TurnAborted(TurnAbortedEvent {
             turn_id: Some(task.turn_context.sub_id.clone()),
             reason,
+            completed_at,
+            duration_ms,
         });
         self.send_event(task.turn_context.as_ref(), event).await;
     }

codex-rs/core/src/tasks/regular.rs

@@ -46,6 +46,7 @@ impl SessionTask for RegularTask {
         // not wait on startup prewarm resolution.
         let event = EventMsg::TurnStarted(TurnStartedEvent {
             turn_id: ctx.sub_id.clone(),
+            started_at: ctx.turn_timing_state.started_at_unix_secs().await,
             model_context_window: ctx.model_context_window(),
             collaboration_mode_kind: ctx.collaboration_mode.mode,
         });

codex-rs/core/src/tasks/user_shell.rs

@@ -111,6 +111,7 @@ pub(crate) async fn execute_user_shell_command(
         // freshly reinjected context before the summary/replacement history is applied.
         let event = EventMsg::TurnStarted(TurnStartedEvent {
             turn_id: turn_context.sub_id.clone(),
+            started_at: turn_context.turn_timing_state.started_at_unix_secs().await,
             model_context_window: turn_context.model_context_window(),
             collaboration_mode_kind: turn_context.collaboration_mode.mode,
         });