I recall during setup of my DietPi that setting up the USB drive was a ‘one time thing’ that you couldn’t choose to do again later.
As of v120, you can setup a USB drive at any time in dietpi-software > user data location.
When you restore from dietpi-backup, its effectively a system restore.
All files and settings are reverted back to when you made the backup. The only exclusions is data in /mnt. So USB drive data is not backed up. dietpi-sync can be used for that: (resolved) Cannot log in to the MySQL server
My USB drive went bad and now I have no idea if it was set up correctly. I replaced the drive, and when using the diet-pi backup, it had me re-initialize the USB drive.
How do I know if my DietPi is set up to properly write as much as it can to the USB drive instead of creating unnecessary writes to the SD card? I spent days configuring things the way I want and would shudder to think I have to do it all over again…
If you replaced your existing USB drive because it failed, and you did not copy/clone the whole contents to another USB drive, I would highly recommend you reinstall DietPi from scratch. Files and folders that installed programs expect will not exist and you will experience issues.
If you copied/cloned the USB drive to another one. You could of simply powered off the device, then swap the drives over 
. However, as it sounds like you did a dietpi-backup restore, any software that was installed after that restore point will need to be reinstalled.
You can check the status of dedicated USB drive in DietPi with:
cat /DietPi/dietpi/.installed | grep USBDRIVE # if this is =2, it means a USB drive was setup by the user
readlink /mnt/dietpi_userdata # If this returns /mnt/usb_1, DietPi is currently using the USB drive for your user data