this is an intriguing idea! I'll admit it's not a direction I've considered taking bitsy in but I can certainly see how it would be cool. that said, it would probably be a pretty large amount of work and maintenance (it requires keeping servers running after all), so I don't see myself having time to take it on in the near term.
I believe it would be possible to hack something like this into a bitsy game once you've exported it as an HTML file, so if you're feeling up to it I definitely encourage you to try to see what you could make! I can point you towards some relevant tutorials too if you decide to try that.
another thought: someday I'd like to add some kind of plugin support to bitsy, and I could see multiplayer/chat being a really neat plugin.
thanks for taking the time to share this suggestion!