Hi diaballein,
Welcome to Apple Support Communities. We understand that you're having an issue with your printer staying connected to your MacBook after updating within macOS Big Sur. We'd like to help.
How is your Printer connected to your MacBook? Is it an AirPrint printer, connected by Wi-Fi, or by an adapter and cable? You mentioned that the drivers are still available, so it's possible that the printer manufacturer has an update available so this doesn't continue to happen when you update your macOS.
Check out these steps on how to Update printer software on Mac. Then, check with your printer manufacturer to see about updates on their end.
Let us know how that goes.
Have a great day!