Bound websocket request sends with idle timeout (#20751)

## Why

We saw Responses websocket sessions recover only after a long quiet
period when the server had already logged the websocket as disconnected.
The normal connect path is already bounded by
`websocket_connect_timeout_ms`, but the first request send on an
established websocket reused only the receive-side idle timeout after
the write completed. If the socket write/pump stalls, the client can sit
in `ws_stream.send(...)` without reaching the existing receive timeout.

codex-rs/codex-api/src/endpoint/responses_websocket.rs

@@ -556,10 +556,15 @@ async fn run_websocket_response_stream(
     trace!("websocket request: {request_text}");
 
     let request_start = Instant::now();
-    let result = ws_stream
-        .send(Message::Text(request_text.into()))
-        .await
-        .map_err(|err| ApiError::Stream(format!("failed to send websocket request: {err}")));
+    let result = tokio::time::timeout(
+        idle_timeout,
+        ws_stream.send(Message::Text(request_text.into())),
+    )
+    .await
+    .map_err(|_| ApiError::Stream("idle timeout sending websocket request".into()))
+    .and_then(|result| {
+        result.map_err(|err| ApiError::Stream(format!("failed to send websocket request: {err}")))
+    });
 
     if let Some(t) = telemetry.as_ref() {
         t.on_ws_request(