I have recently switched desktop environments from Gnome to Plasma (Yay!) and have tried several distributions (Fedora 34, kubuntu 21.04 & finally openSUSE tumbleweed). I liked openSUSE best with YasT controlling most aspects of the OS. However, I cannot seem to activate notification badges (for taskbar app icons) for non-KDE apps.
In System Settings -> Notifications -> Application Settings I can only see the provided KDE apps on openSUSE, whereas on kubuntu I can see all other apps that provide notifications as well and I can activate notification badges for those apps.
The ~/.config/plasmanotifyrc is empty on openSUSE and filled with the apps, for which I have changed the notification settings on kubuntu.

Any idea what could cause this and why these apps (Discord, mailspring, to name a few) do appear in the list in one distro but not in the other? The apps were installed from the official repos from openSUSE plus the community editions but without any difference.

Did you ask your distribution? Usually distribution specific problems should be asked in their specific forum as it is most likely not related to KDE directly