Wire realtime api to core (#12268)

- Introduce `RealtimeConversationManager` for realtime API management 
- Add `op::conversation` to start conversation, insert audio, insert
text, and close conversation.
- emit conversation lifecycle and realtime events.
- Move shared realtime payload types into codex-protocol and add core
e2e websocket tests for start/replace/transport-close paths.

Things to consider:
- Should we use the same `op::` and `Events` channel to carry audio? I
think we should try this simple approach and later we can create
separate one if the channels got congested.
- Sending text updates to the client: we can start simple and later
restrict that.
- Provider auth isn't wired for now intentionally

codex-rs/codex-api/src/endpoint/realtime_websocket/mod.rs

@@ -1,10 +1,10 @@
 pub mod methods;
 pub mod protocol;
 
+pub use codex_protocol::protocol::RealtimeAudioFrame;
+pub use codex_protocol::protocol::RealtimeEvent;
 pub use methods::RealtimeWebsocketClient;
 pub use methods::RealtimeWebsocketConnection;
 pub use methods::RealtimeWebsocketEvents;
 pub use methods::RealtimeWebsocketWriter;
-pub use protocol::RealtimeAudioFrame;
-pub use protocol::RealtimeEvent;
 pub use protocol::RealtimeSessionConfig;