Perennials that I'm currently eating include a wide assortment of wild and domestic greens including some tree leaves, a few nuts from my baby almond tree, fruits including blackberries, currants of various kinds, serviceberries, plums, peaches, and apples. Perennial/perennializing alliums are a steady thing. I eat a few sunchokes but don't care for them all that much. I am beginning to experiment with a few perennial tubers including groundnuts, but I'm just getting started and haven't tasted them yet. Would love to hear what experience others have had with them. This year I started growing Dioscorea batatas with the idea of using the arial bulbils as a perennial food source. I have no idea yet how it will turn out.
I know you excluded animals, but I'm able to feed my dairy goat largely off coppiced Siberian elms and perennial weeds. Plenty of perennials go to the chickens too.