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/events.rs

@@ -1140,6 +1140,7 @@ pub(crate) struct CodexTurnEventParams {
     pub(crate) after_last_sampling_ms: u64,
     pub(crate) sampling_request_count: u32,
     pub(crate) sampling_retry_count: u32,
+    pub(crate) tools_change_count: u32,
     pub(crate) duration_ms: Option<u64>,
     pub(crate) started_at: Option<u64>,
     pub(crate) completed_at: Option<u64>,

codex-rs/analytics/src/facts.rs

@@ -252,6 +252,7 @@ pub struct TurnProfile {
     pub after_last_sampling_ms: u64,
     pub sampling_request_count: u32,
     pub sampling_retry_count: u32,
+    pub tools_change_count: u32,
 }
 
 #[derive(Clone)]

codex-rs/analytics/src/reducer.rs

@@ -3667,6 +3667,7 @@ fn codex_turn_event_params(
         after_last_sampling_ms,
         sampling_request_count,
         sampling_retry_count,
+        tools_change_count,
     } = profile;
     let token_usage = turn_state.token_usage.clone();
     let codex_error = turn_state.codex_error.as_ref();
@@ -3750,6 +3751,7 @@ fn codex_turn_event_params(
         after_last_sampling_ms,
         sampling_request_count,
         sampling_retry_count,
+        tools_change_count,
         duration_ms: completed.duration_ms,
         started_at,
         completed_at: Some(completed.completed_at),

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,
     }
 }