Preheat air fryer to 375°. Separate biscuits. Cut out centers using a 1-inch cutter; save centers. In batches, place doughnuts in a single layer in greased air fryer. Cook until golden brown and puffed, turning once, about 5 minutes. In batches, cook doughnut holes until golden brown, 3-4 minutes., Meanwhile, in a shallow dish, combine sugar and cinnamon. In a separate bowl, mix melted butter and vanilla. Brush doughnuts and doughnut holes with butter; toss in sugar mixture. Serve warm.