Hello redwise,
Thanks for that info and for choosing the Apple Support Communities. If we understand correctly, you are unable to find Desktop files after restoring a backup to your Mac. If you had your Desktop and Documents folder in iCloud Drive, you may have to turn that back on:
"Turn on Desktop and Documents on every Mac that you want to use with iCloud Drive.
1. From your Mac, choose Apple menu > System Settings. In macOS Monterey or earlier, choose Apple menu > System Preferences.
2. Click Apple ID, then click iCloud.
3. Make sure that iCloud Drive is turned on.
4. Next to iCloud Drive, click Options.
5. Choose Desktop & Documents Folders.
6. 
7. Click Done.
If you want to store your files in iCloud Drive and another cloud storage service, you can keep copies of your files in both, but you can't keep folders from a third-party cloud service in iCloud Drive. You can keep your other cloud service folders in a different place on your Mac, like the home folder.
If you already use a feature from another cloud provider that syncs or manages your Desktop and Documents folders, you need to turn it off to use Desktop and Documents."
And here is more info: Add your Desktop and Documents files to iCloud Drive - Apple Support If that is not the case, we recommend seeing the info in this Apple resource on Time Machine: Time Machine troubleshooting on Mac - Apple Support
Cheers!