In order to use the newly introduced CLOSE message, I needed to use the latest version of the WebSocket protocol (see kubernetes/kubernetes#119157). I simply did it by passing the proper header to the connect_get_namespaced_pod_exec method

response = await self.client_ws.connect_get_namespaced_pod_exec(
    name=pod,
    namespace=self.namespace or "default",
    container=container,
    command=command,
    stderr=True,
    stdin=True,
    stdout=True,
    tty=False,
    _headers={"sec-websocket-protocol": "v5.channels.k8s.io"},
    _preload_content=False,
)

However, I was wondering if it could be useful to make the latest version of the protocol the default one for this client.