Setup Assistant / Migration Assistant does a pretty good job of identifying and isolating incompatible software. It will be placed in an "Incompatible Software" folder. I agree the greater number of intervening macOS versions, the greater potential for something to go wrong. The worst that could possibly happen is that it just won't work though.
So I'm wondering where all the printer drivers are stored?
"All over the place" isn't much of an exaggeration.
Perhaps simply import the entire "printers" folder in the Library?
That probably will not work. You can certainly try it though.
I confess as well to being highly irritated that Brother would not even allow me to search for possible drivers compatible with High Sierra for this printer without creating an account opening me up to intrusive nagging, only to learn that it was too much trouble to update their drivers for this printer.
Count your blessings. Literally every other printer manufacturer is worse. A lot worse. As soon as Apple abandoned the printer market, it was a quick race to the bottom for everyone else. Brother makes printers I hate the least, and that's high praise.