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/core/src/codex.rs

@@ -290,6 +290,9 @@ use crate::tools::sandboxing::ApprovalStore;
 use crate::tools::spec::ToolsConfig;
 use crate::tools::spec::ToolsConfigParams;
 use crate::turn_diff_tracker::TurnDiffTracker;
+use crate::turn_timing::TurnTimingState;
+use crate::turn_timing::record_turn_ttfm_metric;
+use crate::turn_timing::record_turn_ttft_metric;
 use crate::unified_exec::UnifiedExecProcessManager;
 use crate::util::backoff;
 use crate::windows_sandbox::WindowsSandboxLevelExt;
@@ -694,6 +697,7 @@ pub(crate) struct TurnContext {
     pub(crate) dynamic_tools: Vec<DynamicToolSpec>,
     pub(crate) turn_metadata_state: Arc<TurnMetadataState>,
     pub(crate) turn_skills: TurnSkillsContext,
+    pub(crate) turn_timing_state: Arc<TurnTimingState>,
 }
 impl TurnContext {
     pub(crate) fn model_context_window(&self) -> Option<i64> {
@@ -783,6 +787,7 @@ impl TurnContext {
             dynamic_tools: self.dynamic_tools.clone(),
             turn_metadata_state: self.turn_metadata_state.clone(),
             turn_skills: self.turn_skills.clone(),
+            turn_timing_state: Arc::clone(&self.turn_timing_state),
         }
     }
 
@@ -1165,6 +1170,7 @@ impl Session {
             dynamic_tools: session_configuration.dynamic_tools.clone(),
             turn_metadata_state,
             turn_skills: TurnSkillsContext::new(skills_outcome),
+            turn_timing_state: Arc::new(TurnTimingState::default()),
         }
     }
 
@@ -2488,6 +2494,7 @@ impl Session {
         turn_context: &TurnContext,
         item: TurnItem,
     ) {
+        record_turn_ttfm_metric(turn_context, &item).await;
         self.send_event(
             turn_context,
             EventMsg::ItemCompleted(ItemCompletedEvent {
@@ -4988,6 +4995,7 @@ async fn spawn_review_thread(
         truncation_policy: model_info.truncation_policy.into(),
         turn_metadata_state,
         turn_skills: TurnSkillsContext::new(parent_turn_context.turn_skills.outcome.clone()),
+        turn_timing_state: Arc::new(TurnTimingState::default()),
     };
 
     // Seed the child task with the review prompt as the initial user message.
@@ -6583,6 +6591,7 @@ async fn try_run_sampling_request(
         sess.services
             .otel_manager
             .record_responses(&handle_responses, &event);
+        record_turn_ttft_metric(&turn_context, &event).await;
 
         match event {
             ResponseEvent::Created => {}