[codex-analytics] feature plumbing and emittance (#16640)

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[//]: # (BEGIN SAPLING FOOTER)
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* #16870
* #16706
* #16641
* __->__ #16640

codex-rs/app-server/src/message_processor.rs

@@ -665,6 +665,16 @@ impl MessageProcessor {
             self.outgoing.send_error(connection_request_id, error).await;
             return;
         }
+        if self.config.features.enabled(Feature::GeneralAnalytics)
+            && let ClientRequest::TurnStart { request_id, .. }
+            | ClientRequest::TurnSteer { request_id, .. } = &codex_request
+        {
+            self.analytics_events_client.track_request(
+                connection_id.0,
+                request_id.clone(),
+                codex_request.clone(),
+            );
+        }
 
         match codex_request {
             ClientRequest::ConfigRead { request_id, params } => {