Well, it is true, but there are a lot of other apps which don’t transfer to new phones. Google’s Authenticator app is such an example.
From what I understand: anything using the Secure Enclave as primary storage cannot be transferred.
You get a notification at the top of the App for a few days to alert you to the transfer.
Mobile BankID (Scandinavian Identity Service), my British Banking app and Okta verify definitely can't transfer to a new phone. I know because I checked recently.
My overall point is: they're not alone, this is a common issue for Apps.
https://apps.apple.com/us/app/google-authenticator/id3884976...
I, like others, stopped using this app because it had dangerous bugs (app could delete the wrong token) and several limitations.
The additional issue mentioned is that while it works great for the MSA account and any boring TOTP you have setup it doesn't work at all for other Azure AD accounts of seemingly any stripe (Corporate Microsoft 365 accounts, B2B, B2C), which is surprising given it is Microsoft's Authenticator and they highly recommend using it, but it fails for Corporate MFA transfers. It just gives an error icon and not very useful error message.