Add exec-server stub server and protocol docs (#15089)

Stacked PR 1/3.

This is the initialize-only exec-server stub slice: binary/client
scaffolding and protocol docs, without exec/filesystem implementation.

---------

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

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

@@ -0,0 +1,38 @@
+use std::sync::Arc;
+
+use crate::protocol::InitializeResponse;
+use crate::server::ExecServerHandler;
+
+use super::ExecServerError;
+
+#[derive(Clone)]
+pub(super) struct LocalBackend {
+    handler: Arc<ExecServerHandler>,
+}
+
+impl LocalBackend {
+    pub(super) fn new(handler: ExecServerHandler) -> Self {
+        Self {
+            handler: Arc::new(handler),
+        }
+    }
+
+    pub(super) async fn shutdown(&self) {
+        self.handler.shutdown().await;
+    }
+
+    pub(super) async fn initialize(&self) -> Result<InitializeResponse, ExecServerError> {
+        self.handler
+            .initialize()
+            .map_err(|error| ExecServerError::Server {
+                code: error.code,
+                message: error.message,
+            })
+    }
+
+    pub(super) async fn initialized(&self) -> Result<(), ExecServerError> {
+        self.handler
+            .initialized()
+            .map_err(ExecServerError::Protocol)
+    }
+}