Airport Time Capsule backs up MacBook Pro but not iMac

Thanks for the info. Don't mean to be technical here, but some explanation is needed to try to understand what is really going on with Big Sur.

The hard drive on your Big Sur Mac was changed from a previous format of Mac OS Extended (Journaled) to another format called APFS when you updated to Big Sur. But....the Time Capsule hard drive cannot be formatted in APFS, it must remain formatted in Mac OS Extended (Journaled).

To try to back up a Big Sur Mac on the Time Capsule, Apple is performing some tricks to store the backup of the Big Sur Mac in a special container called a "backupbundle" that is formatted in APFS on the Time Capsule hard drive....which is formatted differently in Mac OS Extended (Journaled). Gosh, wonder what could possibly go wrong with this type of goofy setup.

This is working for some users, but not others.....like me. You will have much better luck if you simply attach a USB drive directly to the iMac, format the drive in APFS and back up to the hard drive. In other words, leave the Time Capsule out of the equation.

Can you consider this? The USB drive won't take up much space and could probably be hidden if needed without too much effort. Backups will be much faster this way as well.

I recently noticed that backups for the iMac were not occurring.

What operating system is installed on the iMac?

If you have "updated" to the Big Sur operating system, did the problems start after you did this?

Remember that you may need to format the USB drive in APFS before you run the backup. If it is a new USB drive, Time Machine is supposed to automatically format the drive before the backup runs.