This is not easy to answer as a whole, as it depends on your particular setting. However, here are my thoughts on this:
I think option 2 is a better approach because open connections are indeed a limited resource for many web servers. Remember that a connection to websocket is different from a regular HTTP request and remains open for a long time. The extra complexity of the multiplex protocol is really not a problem, I think. All implementations that I know about communication protocols with websocket use the latter approach, although I must admit that I really do not know many examples.
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