Maybe try pushing them via a `ReadableStream`?

In serverless environments such as Vercel Edge Functions or Cloudflare Workers, WebSocket connections can't outlive a single request. That means Pool or Client objects must be connected, used and closed within a single request handler. Don't create them outside a request handler; don't create them in one handler and try to reuse them in another; and to avoid exhausting available connections, don't forget to close them