Pour olive oil into a large ovenproof skillet or baking dish. Season bass with scallions, salt, pepper, oregano, and lemon and orange zests; place in skillet skin-side up. Pour vermouth over fish.
Top fish with butter and transfer to oven; bake until fish is semi-firm to the touch and just cooked through, about 5 minutes.
Transfer fish to a plate and pour any juices left in baking dish into a small saucepan. Place over low heat and add pesto, whisk until well combined. Stir in basil, parsley, and celery leaves; if mixture seems too thick, add a little hot water to adjust consistency.
Divide pesto mixture evenly between four plates and top with fish fillets. Serve immediately.