How to restore the previous version of Mac OS Catalina from Big Sur
How to restore the previous version of Mac OS Catalina from Big Sur
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Here's some info.
How to get old versions of macOS - Apple Support
You will need to completely erase the drive to install Catalina.
If you have a Time Machine backup, you can boot into Internet Recovery and restore from your backup after erasing the drive.
If you don't have a backup of Catalina, create a bootable USB installer of Catalina, boot from that, erase the disk, and install Catalina.
Manually move your files from the backup into Catalina.
Some things like Photos Libraries, Music Libraries, Mail, etc. may not have the same storage structure in Catalina, so you might not be able to open those libraries in Catalina. You'd have to export all of the info from the Library in Big Sur, then import it into the Catalina versions.