Unfortunately, Discord offers a .deb package that cannot actually be installed on Debian. The problem is that Discord depends on libappindicator1, which was deprecated over 3 years ago, instead of the replacement, libayatana-appindicator1. As a work around, the dependency can be changed in the .deb file and the application can be installed. Here is the workaround:
dpkg-deb -R discord-0.0.17.deb /tmp/discord-deb
sed -i 's/libappindicator1/libayatana-appindicator1/g' /tmp/discord-deb/DEBIAN/control
dpkg-deb -b /tmp/discord-deb discord-0.0.17-fixed.deb
This will modify your .deb so that it can be installed normally on Debian 11 “Bullseye”. If a newer version has come out and the problem has not been fixed, just change the version numbers in the file name accordingly.
UPDATE: This fix is still necessary for version 0.0.17
UPDATE: The fix is finally no longer needed for version 0.0.18
