I really can't help with the technical questions, but I do have to say I'd be excited for this! I occasionally stream code work on twitch, but it's geared towards higher view counts instead of more interesting comments, and so far dev.to has been full of really insightful people. I'd rather have 1 person from here to talk to during a stream then 10 people on twitch who are looking for something completely different. There's still the science and technology category on twitch if you wanted to do embeds, but it would be nice if dev.to had it's own more specific tagging system for video steams.
Edit: How hard would it be to integrate the chat with something like restream.io?
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