I use appimagelauncher. Whenever you try to open an appimage from the explorer (I'm using nautilus), it pops up and ask if I want to "install" it or just run it.
If I install, it sets up a .desktop file and moves the appimage to an appropriate folder so not only is it organised, but I can search and launch it from the app menu and it deletes the appimage from the downloads folder.
Appimages are the worst of all Linux package management tools. Absolute last resort.
Flatpaks, snaps, whatever your system package manager is. They all have a single central place to update all installed apps. Appimages are windows ME all over again.
It is 2026 and we are going to individual web sites to manually check for updates one app at a time. Who's idea was that and why did anyone listen?
Worst case make your own package repositories, not that hard. The primary thing that annoys me with package managers is no namespacing.
A package repository can override any package name. Which could lead to conflicts on independent sources