Do you mean a flatpak? Flatpaks are notorious for not integrating. Try to see if hidamari is available first as a .deb file in the official repos (uninstall the flatpak first). If that's not it, then it seems that it doesn't work with the Cinnamon desktop, which has control over the wallpaper functions.
I was able to solve the problem. Instead of downloading it from the Software Manager I installed it from the terminal instead.
When I installed it from the software manager it didn't download one of the packages (org.gnome.platform/44) but when I did it from the terminal it did.
Can you elaborate on that? I am a new Linux user and read a lot about flatpaks in the last week. My impression was, that while space demanding, flatpaks are super easy integrated and that's why they are so succcessful?
It depends, since flatpaks are sandboxed, they don't have access to anything by default. The developer can set defaults for what their app is allowed to access and the user can also manually change that. There's also portals, so you can give them access for a file once (e.g. when opening in a file in an app) or allow them to see your screen and so on. There's still a lot of things that don't have portals tho, so flatpaks don't have access to that.
It's not false information. There are a lot of system-oriented things that don't work through appimages or snaps or flatpaks, exactly because they're sandboxed.