FWIW, with a Discord install from a .rpm made with RPM Outpost's discord rpm maker[1], Discord works perfectly for me on Fedora. The only issues I've had is when I used the flatpak. Though I do suppose Discord should take some flak for only providing .deb files.

[1] https://github.com/RPM-Outpost/discord

P.S. I run a repo that provides Discord, ArmCord, th-ch/youtube-music, and appimagelauncher for Fedora: https://askiiart.net/repos/fedora/x86_64/askiiart.repo

Well, it provides whatever I feel like adding. I'm a pretty bad maintainer, but Discord is always up-to-date, at least.

Does screen sharing with desktop audio work?

Yep, works perfectly. I had issues at some point, but it's fixed now.