an update
it’s pretty fiddly to actually get this all working.
the basic audio setup I have is one semi-decent mic (AKG C1000S), in front of the amp, going into a semi-decent soundcard box (focusrite 2i2). the card goes into macbook pro.
the simple option is: youtube. you need to wait 24 hours to have live streaming enabled on the account, but then it all just works in the browser. chrome-only, though. however, the sound quality is pretty terrible. maybe fine for unboxing videos or whatever, but pretty awful to actually try to play music.
the more complicated version: twitch.
you can’t really use twitch directly in the browser, you need to use some kind of external software. (or rather, there is an option to run it in the browser via another thing called lightstream, but I couldn’t figure out how to use that without having to sign up for a paid account).
the main streaming thing for twitch is twitch studio. but I’m running mac os 10.13. the twitch studio app only runs in 10.14+. but, confusingly, the twitch app (as opposed to the twitch studio app) runs fine on 10.13. but you apparently can’t stream from that. I suppose it’s just for watching other people’s streams or whatever the kids are up to.
so I installed OBS. again, there are seemingly two things, OBS and OBS streamlabs, again with two different supported versions of mac OS.
OBS is seriously clunky-looking, but then it’s open-source stuff for nerds that want to get fussy.
so I fiddled with it all and started streaming through OBS to a twitch account (to do this you need to connect one to the other with a token) and checked the stream. the sound was ok, but it was only coming out one channel. some searching online reveals that it often does this with mono inputs. so.... more searching in the OBS settings, and I got it more-or-less fixed with a stereo-to-mono option in the advanced audio settings. the sound quality is still not great, but better than youtube.
also in the middle of all this I tried to track down an ethernet-to-thunderbolt dongle (so I can connect straight to the router and not rely on wi-fi). but of course all thunderbolt dongles have been banished from the known universe because apple has gone all-in on USB-C. you can still order them online but they’re not in shops anymore. my fault for choosing the apple jail over the PC jail.
so far I feel like I’m still just getting my head around the basics, but hopefully this might be useful to someone. it’s a bit weird that twitch won’t just let you do this in the browser but I suppose their main user base is gamers, who... hate browsers or something. anyway, there’s my outline of the basics, thanks for coming to my ted talk