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Project-Lightspeed
A self contained OBS -> FTL -> WebRTC live streaming server. Comprised of 3 parts once configured anyone can achieve sub-second OBS to the browser livestreaming
jellyfin can certainly do what you are looking for, but it seems like you probably don't have enough bandwidth to reliably host the service at home, and may be overkill for your usage... you could set up project lightspeed (https://github.com/GRVYDEV/Project-Lightspeed) on a $5/month VPS and use OBS to stream video with sub 1 second latency, you can install teamspeak or mumble or something on the same VPS for voice chat.
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