Context of issue
The MFA database is shared between BO and FO for all users, including the admin population.
However, the encryption keys used for this shared database are not shared for the admin population.
As a result, the first environment (BO or FO) that creates a login uses its own encryption key, and the other environment cannot read the key if the same login exists.
Fix required
The MFA for the admin population must not use the shared MFA database. It should use the internal MFA database instead.
Sharing MFA encryption keys is problematic, as each admin environment needs to be independent.