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/protocol.rs

@@ -1,33 +1,15 @@
-use serde::Deserialize;
+pub use codex_protocol::protocol::RealtimeAudioFrame;
+pub use codex_protocol::protocol::RealtimeEvent;
 use serde::Serialize;
 use serde_json::Value;
 use tracing::debug;
 
 #[derive(Debug, Clone, PartialEq, Eq)]
 pub struct RealtimeSessionConfig {
-    pub api_url: String,
     pub prompt: String,
     pub session_id: Option<String>,
 }
 
-#[derive(Debug, Clone, PartialEq, Eq, Serialize, Deserialize)]
-pub struct RealtimeAudioFrame {
-    pub data: String,
-    pub sample_rate: u32,
-    pub num_channels: u16,
-    #[serde(skip_serializing_if = "Option::is_none")]
-    pub samples_per_channel: Option<u32>,
-}
-
-#[derive(Debug, Clone, PartialEq, Eq)]
-pub enum RealtimeEvent {
-    SessionCreated { session_id: String },
-    SessionUpdated { backend_prompt: Option<String> },
-    AudioOut(RealtimeAudioFrame),
-    ConversationItemAdded(Value),
-    Error(String),
-}
-
 #[derive(Debug, Clone, Serialize)]
 #[serde(tag = "type")]
 pub(super) enum RealtimeOutboundMessage {