When you've confirmed that all of your accounts have transferred and are working on your new phone, you can safely delete the Microsoft Authenticator app from your old phone.

It is important to mention here that the Authenticator app collects Account info you provide when you add your account. If you have any apprehensions regarding this, you can remove it by simply ...

Tap the trashcan. On the confirmation box, tap Remove account. Remember that removing an account from the Google Authenticator app doesn't affect the status of 2FA on the account itself.