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/exec/src/event_processor_with_human_output.rs

@@ -806,6 +806,9 @@ impl EventProcessor for EventProcessorWithHumanOutput {
             | EventMsg::RequestUserInput(_)
             | EventMsg::CollabResumeBegin(_)
             | EventMsg::CollabResumeEnd(_)
+            | EventMsg::RealtimeConversationStarted(_)
+            | EventMsg::RealtimeConversationRealtime(_)
+            | EventMsg::RealtimeConversationClosed(_)
             | EventMsg::DynamicToolCallRequest(_) => {}
         }
         CodexStatus::Running