[stack 2/4] Align main realtime v2 wire and runtime flow (#14830)

## Stack Position
2/4. Built on top of #14828.

## Base
- #14828

## Unblocks
- #14829
- #14827

## Scope
- Port the realtime v2 wire parsing, session, app-server, and
conversation runtime behavior onto the split websocket-method base.
- Branch runtime behavior directly on the current realtime session kind
instead of parser-derived flow flags.
- Keep regression coverage in the existing e2e suites.

---------

Co-authored-by: Codex <noreply@openai.com>

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

@@ -264,9 +264,11 @@ impl ChatWidget {
             RealtimeEvent::SessionUpdated { session_id, .. } => {
                 self.realtime_conversation.session_id = Some(session_id);
             }
+            RealtimeEvent::InputAudioSpeechStarted(_) => {}
             RealtimeEvent::InputTranscriptDelta(_) => {}
             RealtimeEvent::OutputTranscriptDelta(_) => {}
             RealtimeEvent::AudioOut(frame) => self.enqueue_realtime_audio_out(&frame),
+            RealtimeEvent::ResponseCancelled(_) => {}
             RealtimeEvent::ConversationItemAdded(_item) => {}
             RealtimeEvent::ConversationItemDone { .. } => {}
             RealtimeEvent::HandoffRequested(_) => {}