Update realtime handoff transcript handling (#18597)

## Summary

This PR aims to improve integration between the realtime model and the
codex agent by sharing more context with each other. In particular, we
now share full realtime conversation transcript deltas in addition to
the delegation message.

realtime_conversation.rs now turns a handoff into:
```
<realtime_delegation>
  <input>...</input>
  <transcript_delta>...</transcript_delta>
</realtime_delegation>
```

## Implementation notes

The transcript is accumulated in the realtime websocket layer as parsed
realtime events arrive. When a background-agent handoff is requested,
the current transcript snapshot is copied onto the handoff event and
then serialized by `realtime_conversation.rs` into the hidden realtime
delegation envelope that Codex receives as user-turn context.

For Realtime V2, the session now explicitly enables input audio
transcription, and the parser handles the relevant input/output
transcript completion events so the snapshot includes both user speech
and realtime model responses. The delegation `<input>` remains the
actual handoff request, while `<transcript_delta>` carries the
surrounding conversation history for context.

Reviewers should note that the transcript payload is intended for Codex
context sharing, not UI rendering. The realtime delegation envelope
should stay hidden from the user-facing transcript surface, while still
being included in the background-agent turn so Codex can answer with the
same conversational context the realtime model had.

codex-rs/core/tests/suite/realtime_conversation.rs

@@ -2480,7 +2480,7 @@ async fn inbound_handoff_request_starts_turn() -> Result<()> {
     let request = response_mock.single_request();
     let user_texts = request.message_input_texts("user");
     assert!(user_texts.iter().any(|text| text
-        == "<realtime_delegation>\n  <input>user: text from realtime</input>\n</realtime_delegation>"));
+        == "<realtime_delegation>\n  <input>text from realtime</input>\n  <transcript_delta>user: text from realtime</transcript_delta>\n</realtime_delegation>"));
 
     realtime_server.shutdown().await;
     Ok(())
@@ -2562,14 +2562,14 @@ async fn inbound_handoff_request_uses_active_transcript() -> Result<()> {
     let request = response_mock.single_request();
     let user_texts = request.message_input_texts("user");
     assert!(user_texts.iter().any(|text| text
-        == "<realtime_delegation>\n  <input>assistant: assistant context\nuser: delegated query\nassistant: assist confirm</input>\n</realtime_delegation>"));
+        == "<realtime_delegation>\n  <input>ignored</input>\n  <transcript_delta>assistant: assistant context\nuser: delegated query\nassistant: assist confirm\nuser: ignored</transcript_delta>\n</realtime_delegation>"));
 
     realtime_server.shutdown().await;
     Ok(())
 }
 
 #[tokio::test(flavor = "multi_thread", worker_threads = 2)]
-async fn inbound_handoff_request_clears_active_transcript_after_each_handoff() -> Result<()> {
+async fn inbound_handoff_request_keeps_transcript_history_after_each_handoff() -> Result<()> {
     skip_if_no_network!(Ok(()));
 
     let api_server = start_mock_server().await;
@@ -2677,13 +2677,13 @@ async fn inbound_handoff_request_clears_active_transcript_after_each_handoff() -
 
     let first_user_texts = requests[0].message_input_texts("user");
     assert!(first_user_texts.iter().any(|text| text
-        == "<realtime_delegation>\n  <input>user: first question</input>\n</realtime_delegation>"));
+        == "<realtime_delegation>\n  <input>first question</input>\n  <transcript_delta>user: first question</transcript_delta>\n</realtime_delegation>"));
 
     let second_user_texts = requests[1].message_input_texts("user");
     assert!(second_user_texts.iter().any(|text| text
-        == "<realtime_delegation>\n  <input>user: second question</input>\n</realtime_delegation>"));
+        == "<realtime_delegation>\n  <input>second question</input>\n  <transcript_delta>user: first question\nuser: second question</transcript_delta>\n</realtime_delegation>"));
     assert!(!second_user_texts.iter().any(|text| text
-        == "<realtime_delegation>\n  <input>user: first question\nuser: second question</input>\n</realtime_delegation>"));
+        == "<realtime_delegation>\n  <input>second question</input>\n  <transcript_delta>user: first questionsecond question</transcript_delta>\n</realtime_delegation>"));
 
     realtime_server.shutdown().await;
     Ok(())
@@ -3207,11 +3207,11 @@ async fn inbound_handoff_request_steers_active_turn() -> Result<()> {
         !first_texts
             .iter()
             .any(|text| text
-                == "<realtime_delegation>\n  <input>user: steer via realtime</input>\n</realtime_delegation>")
+                == "<realtime_delegation>\n  <input>steer via realtime</input>\n  <transcript_delta>user: steer via realtime</transcript_delta>\n</realtime_delegation>")
     );
     assert!(second_texts.iter().any(|text| text == "first prompt"));
     assert!(second_texts.iter().any(|text| text
-        == "<realtime_delegation>\n  <input>user: steer via realtime</input>\n</realtime_delegation>"));
+        == "<realtime_delegation>\n  <input>steer via realtime</input>\n  <transcript_delta>user: steer via realtime</transcript_delta>\n</realtime_delegation>"));
 
     realtime_server.shutdown().await;
     api_server.shutdown().await;
@@ -3327,7 +3327,7 @@ async fn inbound_handoff_request_starts_turn_and_does_not_block_realtime_audio()
     let first_body: Value = serde_json::from_slice(&requests[0]).expect("parse first request");
     let first_texts = message_input_texts(&first_body, "user");
     let expected_text = format!(
-        "<realtime_delegation>\n  <input>user: {delegated_text}</input>\n</realtime_delegation>"
+        "<realtime_delegation>\n  <input>{delegated_text}</input>\n  <transcript_delta>user: {delegated_text}</transcript_delta>\n</realtime_delegation>"
     );
     assert!(first_texts.iter().any(|text| text == &expected_text));