Preheat the oven to 350 degrees F (175 degrees C). Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add butternut squash, cover, and steam until tender, 8 to 10 minutes. Transfer squash to a large bowl. Add carrot, onion, sour cream, cream of celery soup, and cream of chicken soup to the squash. Mix well. Spread evenly in a 9x13-inch pan. Place stuffing mix in a separate bowl and pour melted butter on top, tossing to coat evenly. Spread on top of vegetable mixture in the pan. Bake in the preheated oven, uncovered, until bubbling and golden brown on top, about 20 minutes.