Desktop showing 2 Hard Drives
After having to downgrade from Big Sur to Catilina my desktop now shows 2 Hard Drives Macantosh HD and Macantosh HD Data as well as something with the name Update
MacBook Pro with Touch Bar
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You should have performed a clean install by first erasing the whole physical drive:
https://support.apple.com/guide/disk-utility/erase-and-reformat-a-storage-device-dskutl14079/mac
See if you can delete the Big Sur "Macintosh HD" and "Macintosh HD - Data" volumes. Just make sure you have a backup of all your data from the Big Sur "Macintosh HD - Data" volume before deleting it. You will need to delete the volumes using Disk Utility. In theory you should not be able to delete the volumes for Catalina while you are booted into Catalina, but I would verify which of those volumes are for Big Sur just to be safe.
The "Update" volume was created by Big Sur and AFAIK the "Update" volume isn't used by Catalina, but I haven't checked the most recent version of Catalina to be sure.
Here is information about the multiple volumes with Catalina and Big Sur:
https://support.apple.com/en-us/HT210650
https://support.apple.com/guide/disk-utility/add-erase-or-delete-apfs-volumes-dskua9e6a110/mac
Edit: added link earlier in my post on how to erase the whole physical drive.