Have you really got CCC and Cookie in Full Disk Access? I'm running both apps, and neither is in either Full Disk Access or Accessibility. As a matter of fact, I've got nothing in Full Disk Access.
One of my CCC backups ran last night but a dialogue box warned that it was not done properly because it did not have Full Disk Access. I manually ran the other backup this morning and got the same caution when I hit "Clone".
Interestingly, opening Full Disk Access and checking the CCC box did not get rid of the caution. I actually had to follow the CCC process of dragging their fish icon into the Full Disk Access window....then everything worked as usual.