Printer manufacturers can be bad about not supplying updated drivers for their products. When I replaced a Mac running High Sierra with one running Ventura, I found there were no Ventura drivers for an all-in-one printer which had served me very well.
Two things can help.
Use AirPrint
If your current printer supports AirPrint, you can use AirPrint to get it working again even without Monterey drivers. The idea behind AirPrint is for the printer to have enough "stuff" built in that you don't need to download or install drivers. If your current printer does not support AirPrint, make sure that your next one does!
There is a long list of Brother printers that support AirPrint in the first Support article linked below. You could also check the Brother Web site to see if they mention AirPrint support as a feature of your printer model.
About AirPrint - Apple Support
Print documents from your Mac - Apple Support
Add a printer to your printer list so you can use it on Mac - Apple Support
Use VueScan
This is a commercial product that supports a large number of old, and otherwise-orphaned, scanners. It's only for scanning, not for printing – so only relevant if your printer is an all-in-one. Note that if your printer does support AirPrint, there may be ways to use AirPrint to get scanning going, too, without the VueScan product.
https://www.hamrick.com/