From experience, Catalina is even picker about the size of the Time Machine drive and I have no idea what algorithm is used to determine the minimum drive size. Some suggestions...
  1. You might try disabling the backup of system files and exclude any other attached drives from the backup set essentially limiting Time Machine to backing up ONLY your data files ie. your user folder. Your system files and applications — particularly those purchased thorough the App Store — can easily be reinstalled from the internet. That will significantly reduce the size of the backup and MAY get you below Time Machine's size requirement.
  2. Move Desktop, Documents, Music library, photos library, [/I]etc.[/I] to your iCloud Drive (System Preferences > iCloud > Cloud Drive), here again this can dramatically reduce the size of the TimeMachine backup data set.
  3. Get a higher capacity Time Machine drive
  4. Forego versioned backups and use Carbon Copy Cloner only

If we knew what it was we were doing, it wouldn't be called research, would it?

— Albert Einstein