Big Sur, Big Problems with Time Capsule

I had the same issue; after upgrading both my and my wife's MacBook Airs to Big Sur, back-ups to Time Capsule weren't working. Fiddled with it off & on for a coupla weeks and discovered the issue was most likely due to Sophos (I'd gotten a hint about that from another thread). Deleted & re-installed Sophos again & again & again - same problem. Used harsh language. Didn't work. Prayed; didn't work. Threatened Air w/going back to my Amiga; didn't work. Let it sit after re-installing Sophos on my Air and it magically began to work. Aha! Downloaded Sophos to wife's Air; didn't work - same problems. Repeated harsh language, threats, etc. then noticed on my Air there were five Sophos files under Security & Privacy - Full Disk Access (where you're instructed to drag/drop files during Sophos install) and on my wife's Air, there were only three Sophos files. When I'd searched Sophos Home Free (using DDG), I found two Sophos sites to download from. Both are certified for-real Sophos download sites, but one of 'em downloads a package that gives you the five files and the other downloads a package that only gives three files. Deleted the Sophos on wife's Air, downloaded from the other site, got the five files where they belong and all is well. Sorry I don't remember which URL I downloaded from.....but DDG it, download & experiment until you get the right number of files from the Sophos install package. I'm thinking that very well may have been the issue I was having w/Big Sur + Time Capsule not backing up + Sophos in the mix. Something in the three-file Sophos package doesn't work & play well w/Time Machine & Big Sur. And they all lived happily ever after. The End.