Use realtime transcript for handoff context (#14132)

- collect input/output transcript deltas into active handoff transcript
state
- attach and clear that transcript on each handoff, and regenerate
schema/tests

codex-rs/tui/src/chatwidget/realtime.rs

@@ -264,6 +264,8 @@ impl ChatWidget {
             RealtimeEvent::SessionUpdated { session_id, .. } => {
                 self.realtime_conversation.session_id = Some(session_id);
             }
+            RealtimeEvent::InputTranscriptDelta(_) => {}
+            RealtimeEvent::OutputTranscriptDelta(_) => {}
             RealtimeEvent::AudioOut(frame) => self.enqueue_realtime_audio_out(&frame),
             RealtimeEvent::ConversationItemAdded(_item) => {}
             RealtimeEvent::ConversationItemDone { .. } => {}