[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/core/src/turn_timing.rs

@@ -1,5 +1,7 @@
 use std::time::Duration;
 use std::time::Instant;
+use std::time::SystemTime;
+use std::time::UNIX_EPOCH;
 
 use codex_otel::metrics::names::TURN_TTFM_DURATION_METRIC;
 use codex_otel::metrics::names::TURN_TTFT_DURATION_METRIC;
@@ -45,6 +47,7 @@ pub(crate) struct TurnTimingState {
 #[derive(Debug, Default)]
 struct TurnTimingStateInner {
     started_at: Option<Instant>,
+    started_at_unix_secs: Option<i64>,
     first_token_at: Option<Instant>,
     first_message_at: Option<Instant>,
 }
@@ -53,10 +56,24 @@ impl TurnTimingState {
     pub(crate) async fn mark_turn_started(&self, started_at: Instant) {
         let mut state = self.state.lock().await;
         state.started_at = Some(started_at);
+        state.started_at_unix_secs = Some(now_unix_timestamp_secs());
         state.first_token_at = None;
         state.first_message_at = None;
     }
 
+    pub(crate) async fn started_at_unix_secs(&self) -> Option<i64> {
+        self.state.lock().await.started_at_unix_secs
+    }
+
+    pub(crate) async fn completed_at_and_duration_ms(&self) -> (Option<i64>, Option<i64>) {
+        let state = self.state.lock().await;
+        let completed_at = Some(now_unix_timestamp_secs());
+        let duration_ms = state
+            .started_at
+            .map(|started_at| i64::try_from(started_at.elapsed().as_millis()).unwrap_or(i64::MAX));
+        (completed_at, duration_ms)
+    }
+
     pub(crate) async fn record_ttft_for_response_event(
         &self,
         event: &ResponseEvent,
@@ -77,6 +94,13 @@ impl TurnTimingState {
     }
 }
 
+fn now_unix_timestamp_secs() -> i64 {
+    let duration = SystemTime::now()
+        .duration_since(UNIX_EPOCH)
+        .unwrap_or_default();
+    i64::try_from(duration.as_secs()).unwrap_or(i64::MAX)
+}
+
 impl TurnTimingStateInner {
     fn record_turn_ttft(&mut self) -> Option<Duration> {
         if self.first_token_at.is_some() {