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/lib.rs

@@ -29,8 +29,6 @@ pub use crate::endpoint::aggregate::AggregateStreamExt;
 pub use crate::endpoint::compact::CompactClient;
 pub use crate::endpoint::memories::MemoriesClient;
 pub use crate::endpoint::models::ModelsClient;
-pub use crate::endpoint::realtime_websocket::RealtimeAudioFrame;
-pub use crate::endpoint::realtime_websocket::RealtimeEvent;
 pub use crate::endpoint::realtime_websocket::RealtimeSessionConfig;
 pub use crate::endpoint::realtime_websocket::RealtimeWebsocketClient;
 pub use crate::endpoint::realtime_websocket::RealtimeWebsocketConnection;
@@ -44,3 +42,5 @@ pub use crate::provider::is_azure_responses_wire_base_url;
 pub use crate::sse::stream_from_fixture;
 pub use crate::telemetry::SseTelemetry;
 pub use crate::telemetry::WebsocketTelemetry;
+pub use codex_protocol::protocol::RealtimeAudioFrame;
+pub use codex_protocol::protocol::RealtimeEvent;