Downgrade from macOS big sur

You can download macOS Catalina from the Mac app store. Just search Catalina and click download on your Mac App Store. After you download it, you need to follow some procedure to make your usb drive a bootable drive. After you have a bootable drive, you can delete the old mac harddisk, and use your usb drive to install a clean new macOS on your hard drive. However, it is hard to explain all the steps in here, so I suggest two videos for you.

https://www.youtube.com/watch?v=dQCp-rQlZuY

https://www.youtube.com/watch?v=Ae_Vm39dxrA

Just watch carefully and see if you can follow along.

I haven't downgraded from Big Sur, but I have experience downgrading to Big Sur from macOS 12 beta. Just need a usb drive, and put the old macOS system in it, then you can use the usb drive to reinstall the old system.

Would not be better to work through whatever issues are happening since the upgrade to Big Sur ?

If you provide details of the issues and year of computer - we are surely able to assist.

This method is possible as per Apple Support Documents >> Revert your Mac to a previous macOS version <<. This is predicated on there being a Time Machine Backup existing and having the previous macOS backup available to be used.