I got the cover, which attaches magnetically and folds to form a stand, from Apple. I have tried multiple settings. If I switch Lock/Unlock on, it both darkens the screen and locks the iPad. Nearly all of the time I use the iPad I'm at home, and don't want to lock it, or more significantly, to have to unlock it, every time I set it down. If I switch Lock/Unlock off, it neither locks the device nor darkens the screen. This is the part that is baffling to me. Why would closing the cover not darken the screen, whether I've elected to have it lock the device or not? To avoid the nuisance of locking and unlocking all the time, I turned Lock/Unlock to off, and then found my battery was running down all the time. On inspection, I see that the screen is brightly lighting the under side of the cover. Now I find that if I set Lock/Unlock to off, I have to remember to press the power button to darken the screen. It turns out that pressing the power button itself does not lock the device as I thought.
This is just so non-intuitive, and I expect Apple devices to be intuitive. Closing the cover should darken the screen and preserve battery, IMHO, regardless of whether it is configured to lock the device.
Thanks for your attention. I appreciate your help, but it appears that this is a design flaw, not a configuration error.