I'll just provide the most important item you'd need to have either done or do with the old phone to recover these items on a new phone, which is to back up the Authenticator to your iCloud account.
Back up account credentials in Microsoft Authenticator - Microsoft Support
Without the backup, a restore isn't possible, so it's pointless to discuss these other steps unless you have or can create the backup from the old phone as Aiden has apparently realized.
The restore item is among others listed in the left-hand pane of that same page if a backup is still possible.
Rob