Melt butter in a large skillet over medium-high heat. Add onion and salt and saute until soft, 5 minutes. Add sausage, break into pieces and sauté until cooked through, 8 minutes.
Add fennel, mushrooms, carrots and thyme; cook, stirring, until softened, 8 minutes (add more butter, 1 Tbsp. at a time, if needed).
Preheat oven to 350°F. Mist a 9-by-13-inch baking dish with cooking spray. Stir crackers into stuffing mixture. If mixture is dry, add mushroom liquid (or broth) to moisten.
Spoon mixture into baking dish and bake until heated through and edges are crunchy, 35 to 45 minutes.