Hello OutlookRestore,
Thank you for reaching out in Apple Support Communities. You mentioned that the authenticator is stating that there's no backup but you can see it on the new device. We're not quite sure what you mean by the authenticator. Can you provide the community additional details of what you're referring to?
If you haven't tried yet, here is the proper steps on how to locate an iOS backup in iCloud:
Find and manage backups stored in iCloud
If you use iCloud Backup, you won't find a list of your backups on iCloud.com. Here's how to find your iCloud backups on your iOS or iPadOS device, Mac, or PC.
On your iPhone, iPad, or iPod touch:
1. Go to Settings > [your name] > iCloud.
2. Tap Manage Account Storage, then tap Backups.
3. Tap a backup to see more details about it, choose which information to back up, or delete the backup.
This information is outlined here: Locate backups of your iPhone, iPad, and iPod touch - Apple Support
If the backup exists, then you'll want to follow these steps on how to restore it to your iPhone:
Restore iPhone from an iCloud backup
1. Turn on a new or newly erased iPhone.
2. Do one of the following:
* Tap Set Up Manually, tap Restore from iCloud Backup, then follow the onscreen instructions.
* If you have another iPhone, iPad, or iPod touch with iOS 11, iPadOS 13, or later, you can use Quick Start to automatically set up your new device. Bring the two devices close together, then follow the onscreen instructions to securely copy many of your settings, preferences, and iCloud Keychain. You can then restore the rest of your data and content to your new device from your iCloud backup.
Or, if both devices have iOS 12.4, iPadOS 13, or later, you can transfer all your data wirelessly from your previous device to your new one. Keep your devices near each other and plugged into power until the migration process is complete.
This information is outlined in this helpful article: Restore all content to iPhone from a backup - Apple Support
We look forward to hearing back from you with an update.
Best regards.
