The Fediverse has its own Twitch-style livestreaming platform called OwnCast:
➡️ @owncast
You can find out more from its official website at https://owncast.online
Because it's part of the Fediverse, you can follow OwnCast accounts from Mastodon etc, and when they go live you will see a post in your timeline to let you know.
For example, the RetroStrangeTV livestream can be viewed at:
➡️ https://live.retrostrange.com
...and it can be followed at:
➡️ @rstv