There's a very critical step missing in this solution. You need to be signed in to change your security settings....and how do you change your security settings....if you can't get logged into Microsoft Authenticator?!
In the OP's blurry picture you can see there's no option to sign in using anything except Microsoft.
Alana Wilson,
If you've either replaced or reset your phone without performing a backup of the old phone's authenticator data and restored to the new one, then the Authenticator app is useless, since the data required to perform authentication using the app is no longer available.
The only way possible to recover your old Microsoft Personal account in this case is to use whatever other authentication and verification options still exist, like Windows Hello Face, Fingerprint or PIN on a trusted device, password, phone number (Text), alternate email, or Recovery code (25-Digit printed or saved offline).
If you have any of these, you can use your PC device by selecting that you don't have the Authenticator (I don't have any of these, or some similar prompt at login), to get a list of these other options to try and use instead if you have them. You'll typically need at least 2 of them to make the security setting changes necessary to remove the outdated authenticator (Send sign-in notification) from the list of verification options.
Also, I recommend turning Two-Step verification - Off, a little further down that same page if you can access it, at least until you've been able to set the Authenticator back up on your new phone and perform the first backup so this situation can't happen again.
Unfortunately, the Authenticator app works differently than most consumer users are used to, since the data it contains isn't actually saved in the app itself, but rather some more secure hardware device within the phone, meaning that once that phone device is either factory reset, destroyed or lost, the authentication data it contained is lost with it.
That's why the phone backup with the Authenticator app data it includes, along with the other backup methods of authentication I mentioned above are all so necessary to recover from situations like a lost damaged or replaced phone.
Rob