The behavior of websockets in this manner is no different then any standard HTTP/HTTPS connection -- only the two endpoints can talk. The client can send bytes to the server, and the server can send bytes to the client. The only way a server could use that mechanism to talk to other machines on the client network is if the client is specifically written to do that.

So, one could write a HTTP-proxy that connects outbound to a websocket and then will execute any http requests pushed to it by the server, but that would require you to explicitly implement such a thing. One can do the same thing over many protocols. The key is it is something the client would have to explicitly implement, not something that you would accidentally enable.