During the pandemic I've been playing puzzle and story games with friends by streaming the game to them over discord. Discord cannot capture the audio of a game in Linux for some reason.

On windows it can capture the audio from that specific window.

You should be able to work around this yourself using a pulseaudio null sink and some loopbacks. You send the game audio to the sink, and loop the audio from the sink back to your main output device. I've done this in the past for OBS, but you should be able to add your microphone input as well using another set of sinks and loopbacks I think.

Sadly this causes discord to noise cancel the game audio and it sounds horrible

Yeah, also the audio codec for voice is really low bitrate so even if you turn off all the filtering in the UI it's still pretty bad, while the proper streaming setup has better audio