What issue are you having with the flatpak? Perhaps it is best to file an issue here https://github.com/containers/podman-desktop/issues/new/choo.... As some details like your distro, versions, etc might help to resolve this.

Since you mention, is the tarball not an option? This is supposed to be portable. What would you prefer?

And on Homebrew, and packaged for Arch and Gentoo, and other comments seem to indicate that there are outdated .debs for Ubuntu/Debian, and not-outdated ones if you are okay with a third-party repo (which isn't that big of a stretch…?)

That seems pretty well packaged, honestly.

What file format would you expect?

AppImage could work, also making it portable.