What kind of tires should I buy for an e-bike, commuting on maintained off-road?
In general, the softer the ground, the bigger the tire should be. A fat tire will let you "float" over the surface instead of sinking in, like a snowshoe. If you're sinking, it takes tremendous effort to keep riding, and you can't really steer. 

Gravels vary widely. Coarse-edged crushed rock locks together to create a firm, traffic-bearing surface. Round-edged "pea gravel" shifts under load, dispersing energy - this is good under playground equipment. There are different sizes, and some are mixed while others are consistently-sized. Which one you're on will have an effect on what kind of tire you need.

I like to choose the fattest tire that works well in my frame / under my fenders. I avoid knobbies because I think they have way higher rolling resistance and wear out faster. Since you're already hauling a battery, you can definitely afford the weight of the rubber.

Also, if you ever find yourself in ground that's too loose and you can't steer, shift your weight back. Unweighting the front wheel will let it steer without sinking.