[rollout-trace] Add x-codex-inference-call-id header to inference calls. (#22311)

This allows us to attach call logs to inference requests in traces.

codex-rs/core/src/client.rs

@@ -1256,7 +1256,7 @@ impl ModelClientSession {
                 self.client.state.auth_env_telemetry.clone(),
             );
             let compression = self.responses_request_compression(client_setup.auth.as_ref());
-            let options = self
+            let mut options = self
                 .build_responses_options(turn_metadata_header, compression)
                 .await;
 
@@ -1269,6 +1269,7 @@ impl ModelClientSession {
                 service_tier.clone(),
             )?;
             let inference_trace_attempt = inference_trace.start_attempt();
+            inference_trace_attempt.add_request_headers(&mut options.extra_headers);
             inference_trace_attempt.record_started(&request);
             let client = ApiResponsesClient::new(
                 transport,