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/common.rs

@@ -1764,6 +1764,7 @@ mod tests {
     use codex_protocol::config_types::MultiAgentMode;
     use codex_protocol::models::BUILT_IN_PERMISSION_PROFILE_READ_ONLY;
     use codex_protocol::parse_command::ParsedCommand;
+    use codex_protocol::protocol::CodexResponseHandoffMode;
     use codex_protocol::protocol::RealtimeConversationVersion;
     use codex_protocol::protocol::RealtimeOutputModality;
     use codex_protocol::protocol::RealtimeVoice;
@@ -3390,6 +3391,7 @@ mod tests {
                 flush_transcript_tail_on_session_end: Some(true),
                 codex_responses_as_items: None,
                 codex_response_item_prefix: None,
+                codex_response_handoff_mode: Some(CodexResponseHandoffMode::BemTags),
                 thread_id: "thr_123".to_string(),
                 model: Some("realtime-treatment-model".to_string()),
                 output_modality: RealtimeOutputModality::Audio,
@@ -3411,6 +3413,7 @@ mod tests {
                     "flushTranscriptTailOnSessionEnd": true,
                     "codexResponsesAsItems": null,
                     "codexResponseItemPrefix": null,
+                    "codexResponseHandoffMode": "bemTags",
                     "model": "realtime-treatment-model",
                     "outputModality": "audio",
                     "includeStartupContext": false,
@@ -3435,6 +3438,7 @@ mod tests {
                 flush_transcript_tail_on_session_end: None,
                 codex_responses_as_items: None,
                 codex_response_item_prefix: None,
+                codex_response_handoff_mode: None,
                 thread_id: "thr_123".to_string(),
                 model: None,
                 output_modality: RealtimeOutputModality::Audio,
@@ -3456,6 +3460,7 @@ mod tests {
                     "flushTranscriptTailOnSessionEnd": null,
                     "codexResponsesAsItems": null,
                     "codexResponseItemPrefix": null,
+                    "codexResponseHandoffMode": null,
                     "model": null,
                     "outputModality": "audio",
                     "includeStartupContext": null,
@@ -3475,6 +3480,7 @@ mod tests {
                 flush_transcript_tail_on_session_end: None,
                 codex_responses_as_items: None,
                 codex_response_item_prefix: None,
+                codex_response_handoff_mode: None,
                 thread_id: "thr_123".to_string(),
                 model: None,
                 output_modality: RealtimeOutputModality::Audio,
@@ -3496,6 +3502,7 @@ mod tests {
                     "flushTranscriptTailOnSessionEnd": null,
                     "codexResponsesAsItems": null,
                     "codexResponseItemPrefix": null,
+                    "codexResponseHandoffMode": null,
                     "model": null,
                     "outputModality": "audio",
                     "includeStartupContext": null,
@@ -3715,6 +3722,7 @@ mod tests {
                 flush_transcript_tail_on_session_end: None,
                 codex_responses_as_items: None,
                 codex_response_item_prefix: None,
+                codex_response_handoff_mode: None,
                 thread_id: "thr_123".to_string(),
                 model: None,
                 output_modality: RealtimeOutputModality::Audio,