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/tests/suite/v2/experimental_api.rs

@@ -74,7 +74,7 @@ async fn realtime_conversation_start_requires_experimental_api_capability() -> R
     let request_id = mcp
         .send_thread_realtime_start_request(ThreadRealtimeStartParams {
             thread_id: "thr_123".to_string(),
-            prompt: "hello".to_string(),
+            prompt: Some(Some("hello".to_string())),
             session_id: None,
             transport: None,
         })
@@ -109,7 +109,7 @@ async fn realtime_webrtc_start_requires_experimental_api_capability() -> Result<
     let request_id = mcp
         .send_thread_realtime_start_request(ThreadRealtimeStartParams {
             thread_id: "thr_123".to_string(),
-            prompt: "hello".to_string(),
+            prompt: Some(Some("hello".to_string())),
             session_id: None,
             transport: Some(ThreadRealtimeStartTransport::Webrtc {
                 sdp: "v=offer\r\n".to_string(),