You are designing an application that uses WebSockets and HTTP sessions that are not distributed...

Google HTTP(S) Load Balancing has native support for the WebSocket protocol when you use HTTP or HTTPS, not HTTP/2, as the protocol to the backend.

Ref: https://cloud.google.com/load-balancing/docs/https#websocket_proxy_support

So the next possible step is to Meet with the cloud enablement team to discuss load balancer options.

We dont need to convert WebSocket code to use HTTP streaming or Redesign the application, as WebSocket support is offered by Google HTTP(S) Load Balancing. Reviewing the encryption requirements is a good idea but it has nothing to do with WebSockets.