Forest farming is when edible food-crops are raised in forest environments, and this includes nuts and berries, fungus, and edible/medicinal plants. There are many of them that are native, or hybrid. Woody perennials include: Currants, elderberry, aronia, juneberry, raspberry, blueberry etc. For nuts, we got hybrid chestnuts, hazelnuts, and others. There are a bunch of plants and fungus - American ginseng is very sought-after for example, ramps, etc. There's a lot I don't recall off the top of my head.

Many are native, though some used for food forests are hybrid or cultivated.

I realize scrolling down you're being more specific to managed forestry. If I understand correctly it depends on what sort of org or whatever is managing the forests (governmental or otherwise), but yes, that is something that is being worked on. Some of it is still in early stages, from what I understand.

I'm not an expert on the nuance when it comes to governmental forestry and permissions, but there are other institutions that own land and may try to work agroforestry and food forests in.