Remove outer handler mutex from exec-server RPC base

Co-authored-by: Codex <noreply@openai.com>

codex-rs/exec-server/src/client/local_backend.rs

@@ -1,7 +1,5 @@
 use std::sync::Arc;
 
-use tokio::sync::Mutex;
-
 use crate::protocol::InitializeResponse;
 use crate::server::ExecServerHandler;
 
@@ -9,24 +7,22 @@ use super::ExecServerError;
 
 #[derive(Clone)]
 pub(super) struct LocalBackend {
-    handler: Arc<Mutex<ExecServerHandler>>,
+    handler: Arc<ExecServerHandler>,
 }
 
 impl LocalBackend {
     pub(super) fn new(handler: ExecServerHandler) -> Self {
         Self {
-            handler: Arc::new(Mutex::new(handler)),
+            handler: Arc::new(handler),
         }
     }
 
     pub(super) async fn shutdown(&self) {
-        self.handler.lock().await.shutdown().await;
+        self.handler.shutdown().await;
     }
 
     pub(super) async fn initialize(&self) -> Result<InitializeResponse, ExecServerError> {
         self.handler
-            .lock()
-            .await
             .initialize()
             .map_err(|error| ExecServerError::Server {
                 code: error.code,
@@ -36,8 +32,6 @@ impl LocalBackend {
 
     pub(super) async fn initialized(&self) -> Result<(), ExecServerError> {
         self.handler
-            .lock()
-            .await
             .initialized()
             .map_err(ExecServerError::Protocol)
     }