This is the first mechanical cleanup in a stack whose higher-level goal is to enable Clippy coverage for async guards held across .await points.

The follow-up commits enable Clippy's await_holding_lock lint and the configurable await_holding_invalid_type lint for Tokio guard types. This PR handles the cases where the underlying issue is not protected shared mutable state, but a tokio::sync::mpsc::UnboundedReceiver wrapped in Arc<Mutex<_>> so cloned owners can call recv().await.

Using a mutex for that shape forces the receiver lock guard to live across .await. Switching these paths to async-channel gives us cloneable Receivers, so each owner can hold a receiver handle directly and await messages without an async mutex guard.

What changed

• In codex-rs/code-mode, replace the turn-message mpsc::UnboundedSender/UnboundedReceiver plus Arc<Mutex<Receiver>> with async_channel::Sender/Receiver.
• In codex-rs/codex-api, replace the realtime websocket event receiver with an async_channel::Receiver, allowing RealtimeWebsocketEvents clones to receive without locking.
• Add async-channel as a dependency for codex-code-mode and codex-api, and update Cargo.lock.

Verification

• The split stack was verified at the final lint-enabling head with just clippy.