Add exec-server filesystem RPC implementation

Layer the filesystem RPC implementation and exec-server-only client cleanup on top of the process RPC follow-up.\n\nCo-authored-by: Codex <noreply@openai.com>

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

@@ -0,0 +1,51 @@
+use codex_app_server_protocol::JSONRPCMessage;
+use codex_app_server_protocol::JSONRPCNotification;
+use codex_app_server_protocol::JSONRPCRequest;
+use codex_app_server_protocol::RequestId;
+use serde::Serialize;
+use tokio::sync::mpsc;
+
+use super::ExecServerError;
+
+pub(super) struct JsonRpcBackend {
+    write_tx: mpsc::Sender<JSONRPCMessage>,
+}
+
+impl JsonRpcBackend {
+    pub(super) fn new(write_tx: mpsc::Sender<JSONRPCMessage>) -> Self {
+        Self { write_tx }
+    }
+
+    pub(super) async fn notify<P: Serialize>(
+        &self,
+        method: &str,
+        params: &P,
+    ) -> Result<(), ExecServerError> {
+        let params = serde_json::to_value(params)?;
+        self.write_tx
+            .send(JSONRPCMessage::Notification(JSONRPCNotification {
+                method: method.to_string(),
+                params: Some(params),
+            }))
+            .await
+            .map_err(|_| ExecServerError::Closed)
+    }
+
+    pub(super) async fn send_request<P: Serialize>(
+        &self,
+        request_id: RequestId,
+        method: &str,
+        params: &P,
+    ) -> Result<(), ExecServerError> {
+        let params = serde_json::to_value(params)?;
+        self.write_tx
+            .send(JSONRPCMessage::Request(JSONRPCRequest {
+                id: request_id,
+                method: method.to_string(),
+                params: Some(params),
+                trace: None,
+            }))
+            .await
+            .map_err(|_| ExecServerError::Closed)
+    }
+}