Preheat the oven (with its two racks evenly spaced apart) to 400°F.
Meanwhile, season the duck with salt and the ground caraway. Heat a large ovenproof nonstick or cast iron skillet over medium heat until warm, then arrange the duck legs in the skillet, skin side down. Cook, resisting the temptation to turn the duck, until the skin is browned, 18–20 minutes. Transfer to a plate, then pour off all but 2 tablespoons of the rendered fat. Return the duck legs to the skillet, skin side up, and nestle the onions around them, cut side down. Transfer the skillet to the oven and cook until the duck skin is deep golden brown, the meat is cooked through, and the onions are tender and browned, 45–50 minutes.
Meanwhile, in a second large, ovenproof nonstick or cast-iron skillet over medium heat, melt the butter. When the foam subsides, add the apples and turn them over in the butter a few times to coat. Arrange the wedges cut side up in the skillet and cook without turning until they begin to brown on the bottom, 5–7 minutes. Transfer the skillet to the oven and cook until the apples are tender and deep golden brown on the bottom, 30–35 minutes.
Transfer the duck legs, onions, and apples to a warmed large platter, garnish with sage leaves, and serve hot.