How to make Microsoft Authenticator: Push Multi-factor authentication (MFA) stay as a sign-in method?

Question

I'm trying to add an account to Microsoft Authenticator on the "Security info" page at mysignins.microsoft.com.

I jump through all the hoops on both the PC and mobile device and get a successful response on both. The method shows up as expected:

However, the second I refresh that page or log out, it is gone:

How do I make this persistent? Thank you.