I had some music playing in the background while testing a Youtube livestream for the first time. Nobody was connected, I was working on camera settings. Google shut it down within a few minutes and bitched at me about a copyright violation. That was the last time I used Youtube.

The platform or the venue pays a more or less flat fee to one or more local copyright associations for music to be played. If you host it yourself, you can get flat-rate streaming licenses (ie. non-seeking linear programming only) for not a lot of money- from a few dozen to some hundreds a year $ depending on location. The DJs should send set lists to their copyright association so that they can remit to the correct people. On e.g. Twitch, the platform should technically handle everything for you via content ID, but they can't catch everything. In any case, the DJ doesn't pay unless they own the performing or broadcasting venue. Streaming service rules on what is allowed also vary depending on the agreements they have set up with the associations.

Instagram has a deal with the record industry. How the renumeration works isn't disclosed but instagram users are allowed to use copyrighted songs as long as they dont use the entire song and the main purpose of the video is to be a video (as opposed to a video that is just a song).

You need to be careful with these; the rules platforms seem to have settled on is that livestreaming is sort of OK but anything which may be archived or replayed isn't. So you get "DJ" and "karaoke" livestreams, but only live.

During lockdown there were things like https://timstwitterlisteningparty.com/ , where the audience comments along but is all synchronously listening to their own copy. I'm still in a group which does this weekly with films.