How to prevent Spotlight searches from waking external HDD

I have a Mac mini running macOS 13.6.5. CCC saves daily backups on an external 4 GB WD HDD and puts the storage device to sleep when done.
Many spotlight searches wake the spinning rust making me wait unnecessarily. I have added the device to the Spotlight privacy setting, and it shows there when the driver is awake (and not, when the drive is not).
How can I prevent spotlight to wake the drive?