Early on I had multiple auth apps on my phone.
Of recent...oh....over 5+ years...my accounts are mostly in Microsoft Authenticator.
I do happen to have DUO on my phone, because we resell DUO to clients that require MFA at their computer login, terminal servers, servers, etc.
We don't have it used for 365 or other things. I only have my clients accounts on DUO and our primary DUO partner account login.
At work we keep our "shared logins" in our documentation/password management system..HUDU.
Back to Microsoft Authenticator, I have around 20x accounts in there....my work 365, my personal 365, my facebook, linked in, Google account, and a whole plethora of accounts for various services I use at the office where I use just my own login....like DNS Filter, SyncroMSP, GravityZone, PAX8, etc etc.
Microsoft Authenticator backs up using your PERSONAL Microsoft account. I initially hated the fact that they didn't allow it to back up to your WORK 365 account. However, I later learned why Microsoft doesn't do that...conflicts with app protection policies and InTune policies...could lead you down a nasty "chicken and the egg" scenario. It does restore quite nicely, a few accounts may need to be re-verified. I've gone through that at least 3 or so times since using Microsoft Authenticator....never lost anything. On the new phone, since the built in phone services can't back up the actual account settings, MS Auth app will be blank...upon first launch, you want to make sure it's not logged in..and choose "restore from backup". That brings you to a wizard to sign into your Microsoft personal account..and then it will restore in a few minutes.
...of course, your Microsoft personal account should be itself secured and MFA'd...if someone busts into that....ugh.
Supporting clients...this is always something to have to deal with whenever they get a new phone. Since most don't know to back it up to a personal account. So it's starting all over again for their 365 account...but that's not really difficult at all. This is one advantage DUO has...within the DUO account, ALL of the accounts within the DUO app are backed up within that a little better...assuming the "enable backup of 3rd party" is enabled in the app. So get a new phone, retore DUO, and they're all back pretty easily.
However, since we're Microsoft-centric...and focus on 365...I like how Microsofts Authenticator app has more features specific for 365 accounts, such as the "numbers matching" way to authenticate, as well as showing the map with the geographic location of the log in attempt. And...the type of app requesting the login. It's pretty slick!