Discord cant stream desktop audio at all on Linux aside from sharing a tab’s audio if you’re using Discord in a web browser. There are custom clients (like discord-screenaudio which OP mentioned) capable of doing this to some extent but they’re based on the web version of discord and lack features / can be buggy. Also these options don’t have hardware encoding so any fast moving content will become a choppy mess for the viewers.
The other alternative on Linux is to just route the app’s audio into your mic source. Others will hear it but it will come out as if its your mic so even those not watching the stream will have to hear the stream audio unless they mute you.