Track inference tool changes in turn analytics (#50964)

## What changed

Add `tools_change_count` to turn profiles and turn analytics events. Compare the full model-visible tool list before each sampling request, retaining the previous list across turns and connection resets. The first list establishes a baseline; subsequent changes increment the current turn's count.

## Testing

Add coverage for schema changes, tool additions, ordering changes, empty lists, and tracking across sessions and transport fallback. Extend the turn event serialization test to include `tools_change_count`.

GitOrigin-RevId: 44a15c42dc7d0b35c166666faeb9627b718b33dd

codex-rs/analytics/src/tests/suite/turns/events_tests.rs

@@ -173,6 +173,7 @@ fn turn_event_serializes_expected_shape() {
             after_last_sampling_ms: 94,
             sampling_request_count: 2,
             sampling_retry_count: 1,
+            tools_change_count: 2,
             duration_ms: Some(1234),
             started_at: Some(455),
             completed_at: Some(456),
@@ -264,6 +265,7 @@ fn turn_event_serializes_expected_shape() {
                 "after_last_sampling_ms": 94,
                 "sampling_request_count": 2,
                 "sampling_retry_count": 1,
+                "tools_change_count": 2,
                 "duration_ms": 1234,
                 "started_at": 455,
                 "completed_at": 456

codex-rs/analytics/src/tests/support.rs

@@ -378,6 +378,7 @@ pub(super) fn sample_turn_profile() -> TurnProfile {
         after_last_sampling_ms: 94,
         sampling_request_count: 2,
         sampling_retry_count: 1,
+        tools_change_count: 2,
     }
 }