Preheat the oven to 400 degrees F. In a small bowl, mix the butter and tarragon until combined; set aside.
Lay out 4 large pieces of foil. Layer the vegetables in the center of each piece of foil, starting with the mushrooms, then the celery and scallions. Dot the vegetables with some of the herb butter (use about half) and season each portion with 1/4 teaspoon salt, and pepper to taste. Lay the tilapia fillets over the vegetables; dot with the remaining herb butter. Sprinkle each fillet with 1/4 teaspoon salt, and pepper to taste.
Bring the foil ends together, fold over and crimp closed on all sides to make sealed packets. Place the packets on a baking sheet and bake until the fish is cooked through but still moist, 18 to 22 minutes. Remove the packets from the oven and let sit 2 minutes before opening. Transfer the fish and vegetables to plates and drizzle with the cooking juices.