I don't have a full answer for you. I think at least some of the problems you are having are related to this item in the Big Sur release notes: If macOS Big Sur 11 beta is installed into the same APFS container as previous versions of macOS, system software updates can no longer be installed on the previous versions of macOS. (64411484) It seems that Big Sur is using an APFS volume format that is not recognized by Catalina. I would tread very carefully here, starting with good backups of your Catalina volume. Then, you might try booting into the recovery partition and seeing if it recognizes the Big Sur volumes properly. If it does you could try deleting them from there. Please understand, I have not tried this myself — it's just an idea.