The firefox snap package uses a number of packages, on 24.10 (oracular) it requires (due connections)
snap:core22
snap:gnome-42-2204
snap:gtk-common-themes
so a 24.10 system which has only firefox snap package added will require those so firefox can run.
A quick look and 22.04 firefox has those same requirements as well.
Ubuntu MATE 22.04 is now End of Life, as being a flavor of Ubuntu Desktop, it came with only 3 years of supported life. This applies to all 22.04 flavors and not just Ubuntu-MATE.
Do note: If you have multiple snap packages that were compiled on different releases; you'll need a Core package for each release the systems were built on; ie. for both 24.10 & 22.04 I've provided here, as the package was built on 22.04 they'll require Core22, but different snap packages may require different Core packages (eg. an older package built on 18.04 may require Core18, not being able to use a Core22 you may already have installed).