Linux is kinda like a 3d printer. You can end up tinkering and tuning more than printing.

2d printers are just cursed and have been since the dawn of mankind though. Go to https://openprinting.org/printers/ and see if your printer is in there and if it is which functionality header it is under. I'm assuming it isn't capable of driverless if debian didn't work and the other distro just happened to have something preinstalled. Unless debian doesn't handle driverless printing out of the box. I've only used debian headless for server stuff so I'm just making assumptions.

Arch maintainers recommend against aur helpers but for quite some time I just did exactly that and got the drivers for whatever jank ass printer I had at the time that way. Most of the official ones I have encountered are rpm and I hadn't used fedora or other rpm distros until recently, and the aur pkgbuilds would unpack the rpm and install the drivers the arch way. Incidentally, last I tried silverblue/ublue/kinoite etc can't install the brother printer rpms via rpm-ostree so having a driverless capable printer was lucky considering it was just randomly given to me by a friend that moved away.

If you share the printer model, someone here can probably also figure out what needs to be done without you having to go through a bunch of troubleshooting too.