One thing to consider is that Elixir/Erlang/the BEAM natively supports clustering. Whether your multiple pods form a cluster from Elixir’s point of view depends on your configuration.
For the LiveView socket state, it is as you started your reasoning: client request reaches your Kubernetes ingress, eventually reaches a Bandit/Cowboy web server in one of the pods, the server returns the “disconnected” rendered HTML, the browser runs JS which connects the socket - it may land on any pod - the server upgrades the connection gets to a WebSocket and the LiveView process and state lives in this pod that served the second “connected” request.
If you have the BEAM setup as a cluster, then processes on different pods can communicate, and for example exchange messages through PubSub.
