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The restore process workflow is different, depending on whether you restore the backup to the same device, or a different device. Only a limited set of data may be restored such as iCloud Photo Library and messages for example.
While it links files and documents, it doesn't typically restore any user data and preferences (think 'look and feel' such as wallpaper, widgets, installed applications, user preferences, and so on). Linking the Apple ID in settings post-setup isn't the same as a restore.
Restoring a backup is only possible during Apple Setup Assistant. When a user restores their content from an iCloud or iTunes backup, there are many considerations to bear in mind: Restoring a backup to an iOS/iPadOS device For more information, visit Back up and recover account credentials in the Authenticator app. If you're using the Microsoft Authenticator app, it's also important to back up your credentials and accounts. Since this screen appears on the device before a wi-fi connection has been established and before the ABM profile has been downloaded, this quick start screen cannot be hidden via ABM.
For details refer to the following Apple support document. Device-to-Device migration as offered on the Quick Start screen after resetting an iOS device isn't supported with Apple Business Manager (ABM).