Microsoft Authenticator accounts won't restore from Cloud.

Yesterday, I successfully restored my iPhone with iOS16.2, all its apps and data, apart from Microsoft Authenticator account details

It had been backed up to iCloud.

The Authenticator app itself has been restored but the saved account codes for VPNs, Facebook etc haven't been restored.

I get a pop-up saying there was a backup on another device, but it's the same device, the same iPhone! It’s as though the Authenticator app and iPhone don't recognize each other any more, even though the Authenticator backup was done on the same iPhone.

Experts. Any ideas or workarounds? I need these account code generators