Route realtime V3 handoffs by response channel (#33903)

## What changed

- Add `codexResponseHandoffMode` to `thread/realtime/start` for V3 sessions, with `thinking` as the default and `commentary` and `bemTags` routing modes.
- Map BEM `analysis` and `commentary` output to the commentary channel and `final` output to the speakable channel, while preserving the original BEM envelope. Unrecognized output falls back to speakable.
- Mark explicit speech appends as speakable and stop adding the legacy `"Agent Final Message"` prefix to V3 handoffs. V1 and V2 continue to ignore the new setting.

## Testing

- Cover channel selection for every routing mode, streamed BEM header parsing, fallback behavior, explicit speech, and V1 compatibility.

GitOrigin-RevId: 1974578257488f2914b252c9c1990ba38831c96b

codex-rs/app-server-protocol/src/protocol/v2/realtime.rs

@@ -1,3 +1,4 @@
+use codex_protocol::protocol::CodexResponseHandoffMode;
 use codex_protocol::protocol::ConversationTextRole;
 use codex_protocol::protocol::RealtimeAudioFrame as CoreRealtimeAudioFrame;
 use codex_protocol::protocol::RealtimeConversationVersion;
@@ -74,12 +75,18 @@ pub struct ThreadRealtimeStartParams {
     /// TODO: Remove this rollout knob once transcript-tail flushing is always enabled.
     #[ts(optional = nullable)]
     pub flush_transcript_tail_on_session_end: Option<bool>,
+    // TODO: Remove this experiment-only delivery path after response-item testing is complete.
     /// Sends automatic Codex responses as realtime conversation items instead of handoff appends.
     #[ts(optional = nullable)]
     pub codex_responses_as_items: Option<bool>,
+    // TODO: Remove this experiment-only prefix with `codex_responses_as_items`.
     /// Optional prefix added to automatic Codex response items when `codexResponsesAsItems` is true.
     #[ts(optional = nullable)]
     pub codex_response_item_prefix: Option<String>,
+    /// Selects how automatic Codex responses are routed in Frameless Bidi sessions. Omitted values
+    /// default to `thinking`. Realtime V1 and V2 ignore this setting.
+    #[ts(optional = nullable)]
+    pub codex_response_handoff_mode: Option<CodexResponseHandoffMode>,
     /// Overrides the configured realtime model for this session only.
     #[ts(optional = nullable)]
     pub model: Option<String>,