Time Machine not working with Big Sur

I've been fighting with this for months, and finally found the cause (at least in my case): I'm running Sophos anti-virus, and this is a known incompatibility with their software and Big Sur which they have documented:

https://support.home.sophos.com/hc/en-us/articles/360051251412-Support-for-macOS-11-Big-Sur-

Here is the full description of the problem from their website:

"Time Machine backups to NETWORK locations (Time Capsule, NAS) are currently failing when Sophos Home is installed on Big Sur macOS 11 - Users will see a message reading "Time Machine couldn't complete the backup - The disk is already in use" This does NOT affect local backups, or backups to external devices/drives. 

This issue is currently under investigation by our development team. As a workaround, run the backup in Safe mode or use an external device to backup to. We expect this issue to be resolved by March of 2021."

I got a different error message (several of them, in fact), but otherwise this matched my problem description. In order to solve this, I had to completely uninstall Sophos. Disabling it wasn't enough. Hopefully they get it worked out, but in the meantime, I'd rather have backups than anti-virus (I'll experiment with other AV solutions).

Hopefully this helps someone else!