AppImage is not what you need. It's just an executable wrapper for the archive. To make the software cross-distro, you need to compile it manually on an old distro with old glibc, make sure all the dependencies are there, and so on.
https://docs.appimage.org/reference/best-practices.html#bina...
There are several automation tools to make AppImages, but they won't magically allow you to compile on the latest Fedora and expect your executable to work on Debian Stable. It's still require quite a lot of manual labor.
Yeah a lot of Appimage developers make assumptions about what their systems have as well (i.e. "if I depend on something that is installed by default on Ubuntu desktop then it's fine to leave out"). For example, a while ago I installed an Appimage GUI program on a headless server that I wanted to use via X11 forwarding. I ended up having to manually install a bunch of random packages (GTK stuff, fonts, etc) to get it to run. I see Appimage as basically the same as distributing Linux binaries via .tar.gz archives, except everything's in a single file.