I hate Microsoft's approach which puts its own MFA app as somehow better than standard TOTP. I want to use standard apps like authy or aegis or even apple passwords app which doesn't require my phone to be connected to the Internet.

I sincerely do not agree with their premise at all.

Coming back to OP, better MFA tools and allowing people to NOT display the verified checkmark should solve the issue? At least talk to the person and hear their grievances.