Might be related here. I also use Debian 10 64 bit and the 4.1.0 AppImage won't start either. Electrum 4.0.9 sitting right next to it fires up just fine! I am not on a machine to use a terminal right now. 4.1.0 AppImage was simply tested by right clicking permissions and making the Image executable.
Thought I would put this on your thread since both of us are using Deb 10 64 bit.
FYI - the AppImage 4.1.0 checks out as GOOD via GPG verify!
Following up from the post above. This is a PATH issue I am running into while running a Buster VM on VirtualBox. If I place the 4.1.0 AppImage on a bare metal Debian Buster it fires right up every single time. Maybe I will get time tomorrow to try and run down how to redirect the "search" for the needed qt files during mount of Electrum 4.1.0 via VirtualBox.
This is beyond me from my current remote location. If anyone has a thought to try tomorrow I'll be back and give it a go.
Unrelated: you may recall that I had an issue with Trezor Suite AppImage as well. I will also see if Suite fires up bare metal too. Now I am starting to think it will. Not available on my current machine!