Trigger greeting after session creation

ws/s2s-ws-client.js

@@ -629,13 +629,16 @@ export class S2sWsRealtimeClient extends EventTarget {
         // out). We only push the user-tunable bits: voice + instructions.
         this._sendSessionUpdate();
         this._sessionConfigured = true;
+        // The s2s server does not echo session.updated. WebSocket messages are
+        // ordered, so this hidden item and response.create are handled only
+        // after the session.update sent immediately above.
+        this._sendStartupGreeting();
         if (this._status === "connecting") this._setStatus("connected");
         break;
 
       case "session.updated":
-        // Wait for this acknowledgement so the real system instructions are in
-        // place before the greeting request warms their prompt prefix.
-        this._sendStartupGreeting();
+        // Some Realtime servers acknowledge session.update; s2s currently does
+        // not. The greeting is already queued from session.created.
         break;
 
       case "input_audio_buffer.speech_started":