The release published on Flathub that you're seeing through Bazaar is very old - I think it's the last open source release.
The AppImage will run on Bazzite, and you could probably also install one of the packages inside a distrobox and export it - Bazzite ships with distrobox installed. The manifest I put together and linked above is also an option and makes it pretty easy to convert your AppImage download to a .flatpak with a few commands - you only need to install flatpak-builder, which is available as a flatpak itself.