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/protocol/src/protocol.rs

@@ -132,7 +132,12 @@ pub struct RealtimeAudioFrame {
 }
 
 #[derive(Debug, Clone, Deserialize, Serialize, PartialEq, Eq, JsonSchema, TS)]
-pub struct RealtimeHandoffMessage {
+pub struct RealtimeTranscriptDelta {
+    pub delta: String,
+}
+
+#[derive(Debug, Clone, Deserialize, Serialize, PartialEq, Eq, JsonSchema, TS)]
+pub struct RealtimeTranscriptEntry {
     pub role: String,
     pub text: String,
 }
@@ -142,7 +147,7 @@ pub struct RealtimeHandoffRequested {
     pub handoff_id: String,
     pub item_id: String,
     pub input_transcript: String,
-    pub messages: Vec<RealtimeHandoffMessage>,
+    pub active_transcript: Vec<RealtimeTranscriptEntry>,
 }
 
 #[derive(Debug, Clone, Deserialize, Serialize, PartialEq, Eq, JsonSchema, TS)]
@@ -151,6 +156,8 @@ pub enum RealtimeEvent {
         session_id: String,
         instructions: Option<String>,
     },
+    InputTranscriptDelta(RealtimeTranscriptDelta),
+    OutputTranscriptDelta(RealtimeTranscriptDelta),
     AudioOut(RealtimeAudioFrame),
     ConversationItemAdded(Value),
     ConversationItemDone {