I think this was the problem, though I’m not quite sure. It may also be related to a system reboot.
GNOME, or at least a portion of it, is crashing a lot. I don’t know the details of what is going on, but I’m not surprised if there are side effects. There is a bug filed on the crash already, which looks like it will be fixed soon!
My discord .desktop file is working now, though the example file is not. I’m happy with this, as I wanted the discord one to work; the example was only for testing.