Unfortunately I have no solution for you; just a commentary on what I and others have experienced in the transitions from Mojave-Catalina-Big Sur regarding Time Machine .sparsebundle and .backupbundle backup files.
Up to Mojave, TM backups were saved as <xxx.sparsebundle>. With the advent of Catalina, TM backups were saved as <xxx.backupbundle>. There followed many complaints that TM backups saved prior to Catalina as .sparsebundle files were not recoverable in Catalina. Some folks claimed that changing the file name extension of pre-Catalina TM backups from .sparsebundle to .backupbundle allowed recovery of pre-Catalina, TM .sparsebundle backups, in Catalina. You may try this approach but this did not work in my case. Fortunately I have a reserve 2015 MBP (Mojave), from which I can recover pre-Catalina TM .sparsebundle files from my Synology NAS.
Now, by Big Sur decree, the TM file name extension reverts to .sparsebundle. One might reasonably expect that by so doing access to pre-Catalina TM .sparsebundle backup files would be possible. I have yet to find a way and I don't know why it does not work. Maybe it's the T2 chip (currently 2019 MBP-Big Sur 11.1) or recent Catalina and Big Sur modifications to APFS and SIP. At their convenience, not ours, Apple may provide a solution.
Your situation is fairly common and another example of how from time to time Apple, apparently without a second thought, cuckolds its clients.
Regards,
Jan.