Clover is always a good choice for ground cover; I also like Alyssum(edible, and smells absolutely wonderful!)
Things to avoid(obvious, I know, but I just have to be thorough):
Root crops
Heavy feeders/water thirsty plants
Invasive Species
Other vining plants (again obvious, but some plants look like bushes or ground-cover, but only because they don't have anything to climb(like jasmine/asparagus fern, etc.))
Growing on my small acre in SW USA; Fruit/Nut trees w/ annuals, Chickens, lamb, pigs; rabbits and in-laws onto property soon.
Long term goal - chairmaker, luthier, and stay-at-home farm dad. Check out my music! https://www.youtube.com/@Dustyandtheroadrunners