Authenticator data synchronization problem on multiple IOS devices

Question

When using Microsoft Authenticator, I encountered the following problems:

I have two mobile phones, iPhone15 and iPhone14, both with Authenticator installed. The two mobile phones are logged in with the same Apple ID, and iCloud synchronization has been turned on. The Authenticator backup and recovery account is also the same.

Problem encountered: I used Authenticator on iPhone15 to add a new 2FA data, but the Authenticator on iPhone14 did not synchronize the newly added data. I can only reinstall Authenticator on iPhone14 and then restore the backup. Synchronize the latest data. Is this a bug? Or is it always like this? Is there something wrong with my understanding of synchronization? Thanks