Move default realtime prompt into core (#17165)

- Adds a core-owned realtime backend prompt template and preparation
path.
- Makes omitted realtime start prompts use the core default, while null
or empty prompts intentionally send empty instructions.
- Covers the core realtime path and app-server v2 path with integration
coverage.

---------

Co-authored-by: Codex <noreply@openai.com>

codex-rs/app-server/README.md

@@ -601,6 +601,9 @@ Then send `offer.sdp` to app-server. Core uses `experimental_realtime_ws_backend
 } }
 ```
 
+Omit `prompt` to use Codex's default realtime backend prompt. Send `prompt: null` or
+`prompt: ""` when the session should start without that default backend prompt.
+
 ```javascript
 await pc.setRemoteDescription({
   type: "answer",