Microsoft Authenicator DOES have a restore feature.

Because Paul as somewhat mentioned that it didn’t have a restore feature, I just wanted to make a note that actually it does. It’s just crazy easy to miss, and if you do, it overwrites your backup. I strongly recommend that you have your current phone available if you mess up so you can quickly restore it if you miss it. The backup is also only good for like devices. Android to Android. IOS to IOS.

When you first log in on your new device on the login screen, the restore from backup option is available in small type. Log in from that option only. If you just log in normally, it will wipe your backup with zero warning.