[codex] Add turn profiling analytics (#26484)

## Summary

Add flat profiling fields to `codex_turn_event` so analytics can explain
where turn wall-clock time is spent without changing tool execution
behavior.

The profile reports:
- time before the first sampling request
- sampling time across all attempts and follow-ups
- overhead between sampling requests
- time blocked in the post-sampling tool drain
- time after the final sampling request
- sampling request and retry counts

## Implementation

- Extend the existing turn timing state with constant-memory phase
accounting and one RAII phase guard.
- Observe sampling and the existing post-sampling drain only at turn
orchestration boundaries.
- Keep tool runtime, tool futures, response item handling, and turn
lifecycle values unchanged.
- Add the profiling fields directly to the existing analytics turn event
without changing app-server protocol or rollout persistence.
- Use the existing turn `status` to distinguish completed, failed, and
interrupted profiles.

Exact sampling/tool overlap is intentionally omitted because measuring
tool completion accurately would require hooks in the tool execution
path.

## Validation

- Add app-server end-to-end coverage for a single-sampling turn with no
blocking tool work.
- Add app-server end-to-end coverage for `request_user_input` blocking
followed by a second sampling request.
- CI is running on the PR; tests were not executed locally per
repository guidance.

codex-rs/analytics/src/events.rs

@@ -817,6 +817,13 @@ pub(crate) struct CodexTurnEventParams {
     pub(crate) output_tokens: Option<i64>,
     pub(crate) reasoning_output_tokens: Option<i64>,
     pub(crate) total_tokens: Option<i64>,
+    pub(crate) before_first_sampling_ms: u64,
+    pub(crate) sampling_ms: u64,
+    pub(crate) between_sampling_overhead_ms: u64,
+    pub(crate) tool_blocking_ms: u64,
+    pub(crate) after_last_sampling_ms: u64,
+    pub(crate) sampling_request_count: u32,
+    pub(crate) sampling_retry_count: u32,
     pub(crate) duration_ms: Option<u64>,
     pub(crate) started_at: Option<u64>,
     pub(crate) completed_at: Option<u64>,