This has nothing to do with Wayland, it's just AppImages kinda sucking. Use Flatpak or the one in your distro's repos, not the AppImage. AppImages are the equivalent of portable apps on Windows, like the single exe ones you'd put on a flash drive to carry around.
Also the AppImage developer is very against Wayland and refuses to support it, which is why Wayland support is a shitshow on AppImages.
If you pick the Flatpak it'll get updated in the background, have a proper launcher and everything.