Only Pod X can only send messages to its client based on WebSocket Protocol as it enables two-way communication between a client to a remote host that has opted-in to communications from that code.

However, in this dev article by Kevin Sookocheff, you may use session affinity that directs traffic from a client to the service pods to optimize and ensure that the same pod receives traffic from the same user. When deploying your service, you can configure session affinity using YAML.