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-protocol/src/protocol/v2.rs

@@ -3854,7 +3854,14 @@ impl From<ThreadRealtimeAudioChunk> for CoreRealtimeAudioFrame {
 #[ts(export_to = "v2/")]
 pub struct ThreadRealtimeStartParams {
     pub thread_id: String,
-    pub prompt: String,
+    #[serde(
+        default,
+        deserialize_with = "super::serde_helpers::deserialize_double_option",
+        serialize_with = "super::serde_helpers::serialize_double_option",
+        skip_serializing_if = "Option::is_none"
+    )]
+    #[ts(optional = nullable)]
+    pub prompt: Option<Option<String>>,
     #[ts(optional = nullable)]
     pub session_id: Option<String>,
     #[ts(optional = nullable)]