After verifying that the user is admin, will you continue to send PM code when logging in? If so, then software without a message receiving mechanism will still not be able to use Fediseer.
I suggest you consider the way I did it in Lemmy Federate. I create a private/public key pair and ask admins to add the public key as a TXT record. If the private key entered while logging in matches the public key in DNS, admin can log in.
This way it is not necessary to query the user with webfinger and send a message. You also avoid the hassle of distinguishing between different messaging structures in the Fediverse.