OS: Zorin OS, but that doesn’t matter because on the screenshot, you can see that the issue still occurs on the “default GNOME panel” when on the App Overview.
I can 100% guarantee that it’s a GNOME problem: Here you can see the exact same AppImage which was integrated using Gear Lever on KDE Plasma, on which the issue didn’t occur:
This is a problem between the app and its .desktop file. If the filename (or StartupWMClass) of the .desktop file does not match the WM_CLASS of the window, gnome-shell won’t associate the window with the app (and therefore app icon).