That’s primarily via the PROs - ASCAP, BMI, SESAC.
E.g. ASCAP says
“Fortunately, most popular live-streaming platforms, such as YouTube, Facebook, Instagram Live, Soundcloud and Twitch are licensed by ASCAP”
I’m assuming because DJ performances via twitch are considered non-interactive streaming they - like Pandora’s free tier - don’t need a mechanical licence, at least in the US.
How that then translates to other territories though I’m not entirely sure. In Europe I’m pretty sure they’d need to have a mechanical licence in place whether or not they are interactive.