Tag tool registration metrics with effective incremental tools mode (#55692)

## What changed

Add an `incremental_tools` attribute to `codex.tools.registered` using the effective mode for the current sampling request. Compute the mode once and reuse it for registration metrics and prompt construction across transport retries.

## Testing

Extend integration tests to verify the attribute for incremental and non-incremental requests, including when the feature flag is enabled but the Responses API does not support incremental tools. Assert registration sample counts and retain coverage that stream retries do not duplicate registration metrics.

GitOrigin-RevId: e5b7a1075fe722ef6bdf900ae07e2b1b06aecfb5

codex-rs/core/src/session/turn.rs

@@ -1742,7 +1742,14 @@ async fn run_sampling_request(
         Arc::clone(&turn_diff_tracker),
     );
     let max_retries = turn_context.provider.info().stream_max_retries();
-    record_registration_metrics(&step_context.tool_router, &step_context.session_telemetry);
+    let incremental_tools = sess
+        .current_window_uses_incremental_tools(&step_context)
+        .await;
+    record_registration_metrics(
+        &step_context.tool_router,
+        &step_context.session_telemetry,
+        incremental_tools,
+    );
     let mut retry_state = ResponsesStreamRetryState::default();
     let mut initial_input = Some(input);
     let mut original_input = None;
@@ -1765,8 +1772,7 @@ async fn run_sampling_request(
             prompt_input,
             step_context.as_ref(),
             base_instructions.clone(),
-            sess.current_window_uses_incremental_tools(&step_context)
-                .await,
+            incremental_tools,
         );
         let responses_metadata = sess
             .responses_metadata(step_context.as_ref(), CodexResponsesRequestKind::Turn)

codex-rs/core/src/tools/router.rs

@@ -395,7 +395,11 @@ impl ToolRouter {
 
 /// Records the registered inventory once per sampling request, before transport retries.
 /// Registrations do not imply model visibility or reachability; hosted tools are excluded.
-pub(crate) fn record_registration_metrics(router: &ToolRouter, telemetry: &SessionTelemetry) {
+pub(crate) fn record_registration_metrics(
+    router: &ToolRouter,
+    telemetry: &SessionTelemetry,
+    incremental_tools: bool,
+) {
     let mut direct = 0usize;
     let mut direct_model_only = 0usize;
     let mut deferred = 0usize;
@@ -418,6 +422,7 @@ pub(crate) fn record_registration_metrics(router: &ToolRouter, telemetry: &Sessi
         ToolMode::CodeMode => "code_mode",
         ToolMode::CodeModeOnly => "code_mode_only",
     };
+    let incremental_tools = if incremental_tools { "true" } else { "false" };
     for (exposure, count) in [
         (EXPOSURE_DIRECT, direct),
         (EXPOSURE_DIRECT_MODEL_ONLY, direct_model_only),
@@ -430,7 +435,11 @@ pub(crate) fn record_registration_metrics(router: &ToolRouter, telemetry: &Sessi
             TOOL_REGISTRATIONS_METRIC,
             i64::try_from(count).unwrap_or(i64::MAX),
             TOOL_REGISTRATIONS_METRIC_BUCKETS,
-            &[("exposure", exposure), ("tool_mode", tool_mode)],
+            &[
+                ("exposure", exposure),
+                ("tool_mode", tool_mode),
+                ("incremental_tools", incremental_tools),
+            ],
         );
     }
 }