What about sliced veggies with a dip like hummus (Ina has a good recipe, or pick some up from a Middle Eastern market) or labneh (Alison Roman’s recipe is great).
Spinach artichoke dip would also qualify as a veggie side.
I would do some sort of cucumber salad, which compliments chili and cornbread. And I think cucumber can also go with some Korean flavors. Something a bit tangy with a vinegar dressing.