Clarify realtime v2 context and handoff messages (#17896)

## Summary
- wrap realtime startup context in
`<startup_context>...</startup_context>` tags
- prefix V2 mirrored user text and relayed backend text with `[USER]` /
`[BACKEND]`
- remove the V2 progress suffix and replace the final V2 handoff output
with a short completion acknowledgement while preserving the existing V1
wrapper

## Testing
- cargo test -p codex-api
realtime_v2_session_update_includes_background_agent_tool_and_handoff_output_item
-- --exact
- cargo test -p codex-app-server webrtc_v2_background_agent_
- cargo test -p codex-app-server webrtc_v2_text_input_is_
- cargo test -p codex-core conversation_user_text_turn_is_

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

@@ -1670,7 +1670,7 @@ mod tests {
             );
             assert_eq!(
                 third_json["item"]["output"],
-                Value::String("\"Agent Final Message\":\n\ndelegated result".to_string())
+                Value::String("delegated result".to_string())
             );
         });
 

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

@@ -45,9 +45,11 @@ 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::V1 => v1_conversation_handoff_append_message(
+            handoff_id,
+            format!("{AGENT_FINAL_MESSAGE_PREFIX}{output_text}"),
+        ),
         RealtimeEventParser::RealtimeV2 => {
             v2_conversation_handoff_append_message(handoff_id, output_text)
         }