The ms authenticator works in 'reverse' in that you type the code on the screen into the phone. I assume this is preferable to corporate as you can't be social engineered into giving out a 2fa token. It also has a "no this wasn't me" button to allow you to (I assume) notify IT if you are getting requests that are not you.
I don't believe that the authenticator app gives them access to anything on your phone? (Happy to learn here) And I think android lets you make some kind of business partition if you feel the need to?
They said that the option to use other authenticators were disabled by their company