feat(otel, core): record turn TTFT and TTFM metrics in codex-core (#13630)

### Summary
This adds turn-level latency metrics for the first model output and the
first completed agent message.
- `codex.turn.ttft.duration_ms` starts at turn start and records on the
first output signal we see from the model. That includes normal
assistant text, reasoning deltas, and non-text outputs like tool-call
items.
- `codex.turn.ttfm.duration_ms` also starts at turn start, but it
records when the first agent message finishes streaming rather than when
its first delta arrives.

### Implementation notes
The timing is tracked in codex-core, not app-server, so the definition
stays consistent across CLI, TUI, and app-server clients.

I reused the existing turn lifecycle boundary that already drives
`codex.turn.e2e_duration_ms`, stored the turn start timestamp in turn
state, and record each metric once per turn.

I also wired the new metric names into the OTEL runtime metrics summary
so they show up in the same in-memory/debug snapshot path as the
existing timing metrics.

codex-rs/otel/src/metrics/names.rs

@@ -20,3 +20,5 @@ pub(crate) const RESPONSES_API_ENGINE_IAPI_TBT_DURATION_METRIC: &str =
     "codex.responses_api_engine_iapi_tbt.duration_ms";
 pub(crate) const RESPONSES_API_ENGINE_SERVICE_TBT_DURATION_METRIC: &str =
     "codex.responses_api_engine_service_tbt.duration_ms";
+pub(crate) const TURN_TTFT_DURATION_METRIC: &str = "codex.turn.ttft.duration_ms";
+pub(crate) const TURN_TTFM_DURATION_METRIC: &str = "codex.turn.ttfm.duration_ms";

codex-rs/otel/src/metrics/runtime_metrics.rs

@@ -10,6 +10,8 @@ use crate::metrics::names::SSE_EVENT_COUNT_METRIC;
 use crate::metrics::names::SSE_EVENT_DURATION_METRIC;
 use crate::metrics::names::TOOL_CALL_COUNT_METRIC;
 use crate::metrics::names::TOOL_CALL_DURATION_METRIC;
+use crate::metrics::names::TURN_TTFM_DURATION_METRIC;
+use crate::metrics::names::TURN_TTFT_DURATION_METRIC;
 use crate::metrics::names::WEBSOCKET_EVENT_COUNT_METRIC;
 use crate::metrics::names::WEBSOCKET_EVENT_DURATION_METRIC;
 use crate::metrics::names::WEBSOCKET_REQUEST_COUNT_METRIC;
@@ -49,6 +51,8 @@ pub struct RuntimeMetricsSummary {
     pub responses_api_engine_service_ttft_ms: u64,
     pub responses_api_engine_iapi_tbt_ms: u64,
     pub responses_api_engine_service_tbt_ms: u64,
+    pub turn_ttft_ms: u64,
+    pub turn_ttfm_ms: u64,
 }
 
 impl RuntimeMetricsSummary {
@@ -64,6 +68,8 @@ impl RuntimeMetricsSummary {
             && self.responses_api_engine_service_ttft_ms == 0
             && self.responses_api_engine_iapi_tbt_ms == 0
             && self.responses_api_engine_service_tbt_ms == 0
+            && self.turn_ttft_ms == 0
+            && self.turn_ttfm_ms == 0
     }
 
     pub fn merge(&mut self, other: Self) {
@@ -90,6 +96,12 @@ impl RuntimeMetricsSummary {
         if other.responses_api_engine_service_tbt_ms > 0 {
             self.responses_api_engine_service_tbt_ms = other.responses_api_engine_service_tbt_ms;
         }
+        if other.turn_ttft_ms > 0 {
+            self.turn_ttft_ms = other.turn_ttft_ms;
+        }
+        if other.turn_ttfm_ms > 0 {
+            self.turn_ttfm_ms = other.turn_ttfm_ms;
+        }
     }
 
     pub fn responses_api_summary(&self) -> RuntimeMetricsSummary {
@@ -137,6 +149,8 @@ impl RuntimeMetricsSummary {
             sum_histogram_ms(snapshot, RESPONSES_API_ENGINE_IAPI_TBT_DURATION_METRIC);
         let responses_api_engine_service_tbt_ms =
             sum_histogram_ms(snapshot, RESPONSES_API_ENGINE_SERVICE_TBT_DURATION_METRIC);
+        let turn_ttft_ms = sum_histogram_ms(snapshot, TURN_TTFT_DURATION_METRIC);
+        let turn_ttfm_ms = sum_histogram_ms(snapshot, TURN_TTFM_DURATION_METRIC);
         Self {
             tool_calls,
             api_calls,
@@ -149,6 +163,8 @@ impl RuntimeMetricsSummary {
             responses_api_engine_service_ttft_ms,
             responses_api_engine_iapi_tbt_ms,
             responses_api_engine_service_tbt_ms,
+            turn_ttft_ms,
+            turn_ttfm_ms,
         }
     }
 }