Welcome and hello!
Maybe a way to think about the whole of your lot is in terms of direct vs indirect productivity. There will be plants that you personally may not be eating, but that attract pollinators, provide for wildlife, or benefit the soil. Perhaps the dogwood falls into the indirect benefit column.
Dogwoods have a lot of value as medicinal plants, and serve as a year round food source for wildlife. I also understand that they "mine" calcium from the soil and rocks and drop it in their leaves to mineralize the topsoil. They are important to the balance and health of the eastern forest and are under pressure from a fungus that has killed a lot of dogwoods in some areas. So in some ways, you have a treasure on your property!
As far as how to plant beneath it most effectively: hostas are shade-loving lower growing plants that are edible when their shoots are still furled ( I think they are related to asparagus and I've seen them cook as you would asparagus). I know they grow well in the Appalachian region. Nasturtium, lettuces and greens that bolt in heat like spinach and arugula, chives, and parsley have grown well for me in shaded spots (you may have to run some ducks through the area to keep down the slug population though

) . I understand sweet potatoes can tolerate some shade but would probably need to be grow in mounded soil rather than digging into the root area of the tree repeatedly. Trellising peas and beans in its dappled shade, using the trunk as the center spoke, may also prolong their growing season when it gets really hot, depending on your specific micro-climate. My grandmother grew amazing raspberries in a semi shaded area of her yard too - ah, the memories that evokes!
I'd also love to get my hands on some wood nettles - I can never get enough nettles in springtime.
I haven't personally gardened in that region for quite a while, so I am certainly missing some good ideas. Hopefully some more experienced with your specific situation will weigh in as well!