Some things that I have tried which didn't immediately fix the problem.
----
Resetting the bluez package did NOT fix the problem.
Removing the bluez package(s), removing /var/lib/bluetooth and re-installing.
The bluetooth system needs to be started, and this empties the list of discovered bluetoothe devices,
but the popup for the keyboard auth number still disappears quickly again.
Some things that I have tried which didn't immediately fix the problem.
----
Resetting the bluez package did NOT fix the problem.
Removing the bluez package(s), removing /var/lib/bluetooth and re-installing.
sudo apt remove --purge bluez -sendto
rm -rf /var/lib/bluetooth
sudo apt install bluez gnome-bluetooth gnome-bluetooth
The bluetooth system needs to be started, and this empties the list of discovered bluetoothe devices,
but the popup for the keyboard auth number still disappears quickly again.