Unless you want to keep Big Sur and have sufficient storage to create a new logical partition adjacent to it for a Catalina installation, you must wipe the Big Sur installation as part of the roll back procedure, as one cannot just install Catalina over Big Sur.
The ideal tool for this is Time Machine, which after booting into Recovery, you request that it Restore from a Time Machine backup — provided you made a Time Machine backup of Catalina before upgrading to Big Sur. Under those conditions, the restore from Time Machine would remove Big Sur and repave the partition with Catalina exactly as it was from the last Time Machine backup, including all of your user data and configuration settings.
Without a Time Machine backup of Catalina, a rollback from Big Sur means wiping the drive, installing Catalina, and then restoring from Google Drive. That is not supported by Apple and if Google Drive changes any of the access control settings or other extended attributes on what you backed up, your Catalina installation will be frought with risk and potentially things that don't work.