Preheat oven to 375 degrees F (190 degrees C). Spray a 9-inch pie dish with cooking spray.
Place the flour, rolled oats, coconut, 1/4 cup of white sugar, 1/4 cup of light brown sugar, 1/2 teaspoon of cinnamon, 1/4 teaspoon of nutmeg, baking powder, baking soda, salt, and butter into the work bowl of a food processor. Pulse several times to make a mixture that looks like coarse crumbs. Stir in the walnuts.
In a large bowl, mix together the apples, 1/4 cup of white sugar, 1/4 cup of brown sugar, tapioca, vanilla extract, 1/2 teaspoon of cinnamon, and 1/4 teaspoon of nutmeg until well combined. Pour the filling into the prepared pie dish; spread the topping evenly over the filling.
Bake in the preheated oven until the apple crisp is bubbling and golden brown, 30 to 40 minutes.