Given that the WebSocket request is “network” compatible with HTTP/1.1 and then it upgrades, it should be compatible with normal HTTP routing, thus all options should apply – at least to the initial connection request.
How to achieve sticky sessions could be accomplished like in case of normal HTTP sticky sessions, which I’ve recently described in another reply:
Although given this is (presumably) a newly developed application, I think it is a considerable design flaw to require sticky sessions.