Don't waste your time looking for a list of error code messages.......Apple does not bother with things like this.
Since you have already restarted your Mac and TC, the next check would be to find out whether Catalina has messed up your backups.....as it has been known to do for some folks.
Hold down the option key on your Mac while you click on the Time Machine "clock" icon at the top of the Mac's screen
Click on Verify Backups
The process might take anywhere from 10-60 minutes or more depending on how much data is stored on the TC disk. Let the process run until it completes or until you receive another error message.
Post back when the process has run. If an error message does appear, post back with the exact text of the message.