I'm not the developer but I'd venture that it's a WebRTC "metadata track" over the same MediaStream the audio is going through.

Metadata tracks aren't formally part of the spec but there's ways to either inject it into the video frame data payload or encode them to audio.

There's libraries like LiveKit that abstract this and make meta tracks easy.

the game doesn't play or stream any audio (though i think maybe a countdown timer or other fun sound effects would be nice)

players usually either a) play in real life on their phones or b) use something like Google Meet or Discord to sing their lyrics

that being said, the "buzz in" feature is sensitive to latency (but, in my experience, it usually takes players a few seconds to think of a song that fits the target word anyway)

It isn't a karaoke game there are no lyrics to sync.