Are all files on that drive denying you write access? Or only specific ones?
Have you been able to change these files at all since installing Big Sur? Was the last time you touched them before you upgraded?
Since a few major macOS versions ago, the new System Integrity Protection feature prevents you from editing certain system files even if you have admin/sudo/root-level permissions. If it's only specific files, I wonder if this is a recent change to SIP in Big Sur. It's a pain in the ass, but you could try disabling it temporarily
to see if that helps.
Meanwhile, to get more info about the drive, open up a terminal window and use this command to get a list of all attached disks:
Find the "IDENTIFIER" for the problematic drive/partition, and use this command, swapping "disk1s1" with yours
diskutil info /dev/disk1s1
What does that give you? Does it have any "Read-Only Media" values with "Yes"?