The biggest problem with this project is that I don't know enough WebSocket to understand if I'm doing something wrong or the server is broken.
I think I figured it out:
I was checking WebSocket wiki page (https://en.wikipedia.org/wiki/WebSocket) and it has a JS example.
And then it hit me: I can do the same with the webdev console. And there, Firefox is complaining that it can connect to the service.
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