Add final message prefix to realtime handoff output (#15077)

- prefix realtime handoff output with the agent final message label for
both realtime v1 and v2
- update realtime websocket and core expectations to match

codex-rs/codex-api/src/endpoint/realtime_websocket/methods.rs

@@ -1173,7 +1173,10 @@ mod tests {
             let fourth_json: Value = serde_json::from_str(&fourth).expect("json");
             assert_eq!(fourth_json["type"], "conversation.handoff.append");
             assert_eq!(fourth_json["handoff_id"], "handoff_1");
-            assert_eq!(fourth_json["output_text"], "hello from codex");
+            assert_eq!(
+                fourth_json["output_text"],
+                "\"Agent Final Message\":\n\nhello from codex"
+            );
 
             ws.send(Message::Text(
                 json!({
@@ -1504,7 +1507,7 @@ mod tests {
             );
             assert_eq!(
                 third_json["item"]["output"],
-                Value::String("delegated result".to_string())
+                Value::String("\"Agent Final Message\":\n\ndelegated result".to_string())
             );
         });
 

codex-rs/codex-api/src/endpoint/realtime_websocket/methods_common.rs

@@ -12,6 +12,7 @@ use crate::endpoint::realtime_websocket::protocol::RealtimeSessionMode;
 use crate::endpoint::realtime_websocket::protocol::SessionUpdateSession;
 
 pub(super) const REALTIME_AUDIO_SAMPLE_RATE: u32 = 24_000;
+const AGENT_FINAL_MESSAGE_PREFIX: &str = "\"Agent Final Message\":\n\n";
 
 pub(super) fn normalized_session_mode(
     event_parser: RealtimeEventParser,
@@ -38,6 +39,7 @@ pub(super) fn conversation_handoff_append_message(
     handoff_id: String,
     output_text: String,
 ) -> RealtimeOutboundMessage {
+    let output_text = format!("{AGENT_FINAL_MESSAGE_PREFIX}{output_text}");
     match event_parser {
         RealtimeEventParser::V1 => v1_conversation_handoff_append_message(handoff_id, output_text),
         RealtimeEventParser::RealtimeV2 => {