MFA stuck at "Finish Enrolling Device"

I’ve hit the same case some others seem to find themselves occasionally where their TOTP MFA status is “Enrollment not complete” and there is a “Finish Enrolling Device” button, but all that happens is the generation of a new recovery code.
Can someone help, please?

Hey there!

Think you’ll be stuck in a loop. Just follow this procedure and we’ll be able to get you out of there: