Hi namer707
Welcome to Microsoft Community.
Based on your description, I understand that you deleted the Desktop folder from OneDrive and then restored it in the notification you received, but at this point the restored folder doesn't have a desktop icon anymore. I understand very well how you feel!
Based on the information you provided, I experimented with an HP laptop and found that after receiving the notification to restore the file, the folder does seem to not have a desktop-like icon, just a regular folder icon, but I tested it and found a solution that should be able to go over and help you with this issue!
After recover the folder, click OneDrive in the taskbar -> click the “Gear” button in the upper right corner -> click “Settings”, then OneDrive Settings will be opened -> in the left sidebar Select “Sync and backup” in the left sidebar -> Select “Manage backup” -> A dialog box will open, please wait for a moment, and then select “Desktop” from the list button and reopen it.
You can refer to the following picture:
After following the above steps, you should be able to see that the recovered folder icon has become a desktop icon instead of a normal folder icon.
I sincerely hope that the above solution will solve your problem. Please feel free to contact me if you encounter any problems.
I look forward to hearing back from you.
Best Regards
Arthur Sheng | Microsoft Community Support Specialist