[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/src/codex_message_processor.rs

@@ -6581,6 +6581,9 @@ impl CodexMessageProcessor {
                     items: vec![],
                     error: None,
                     status: TurnStatus::InProgress,
+                    started_at: None,
+                    completed_at: None,
+                    duration_ms: None,
                 };
 
                 let response = TurnStartResponse { turn };
@@ -6917,6 +6920,9 @@ impl CodexMessageProcessor {
             items,
             error: None,
             status: TurnStatus::InProgress,
+            started_at: None,
+            completed_at: None,
+            duration_ms: None,
         }
     }
 
@@ -9566,6 +9572,7 @@ mod tests {
             state.track_current_turn_event(&EventMsg::TurnStarted(
                 codex_protocol::protocol::TurnStartedEvent {
                     turn_id: "turn-1".to_string(),
+                    started_at: None,
                     model_context_window: None,
                     collaboration_mode_kind: Default::default(),
                 },