How to Transfer Microsoft Authenticator Data Between Two iPhones Without Overwriting Data

Question

I have two iPhones: one old and one new. I am logged into both phones with different iCloud accounts, and I have Microsoft Authenticator installed on both phones with separate data. Now, I want to move all the account logins from the old Microsoft Authenticator (on the old phone) to the new Microsoft Authenticator (on the new phone).

I have created backups for both Microsoft Authenticator apps, but they are stored in different iCloud accounts. I do not want to overwrite the data on the new Microsoft Authenticator app with the old one; instead, I want to add the data from the old Microsoft Authenticator app to the new one.

I cannot do this manually. How can I do this automatically without losing any data?