I’ve streamed myself playing music several times. First through Discord and later through OBS to Twitch.
Discord has, or at least had at the time, very bad audio quality. There might be options for setting higher quality if you have a paid account but I found it insufficient for music.
Twitch, in my experience, has sound quality comparable to music streaming services. It works really well. I found OBS painless to set up, although it is definitely more complex than just making a conference call.
Regarding @reallyok’s question about streaming multiple people, I’ve never tried it but it looks like the recommended method is to set up an RTMP server which participants can stream to, which then streams to your service of choice.
There are a lot of tutorials on setting this up online.
My understanding is that if you want to avoid things like Twitch or YouTube and still want to use OBS, you would likely need to set one of these up anyway.
I haven’t tried this yet so I may have a lot of details wrong but I’m likely to experiment with it and I’ll report back if I do anything with it.