Stir together pecans, white sugar, and brown sugar for the pecan topping in a small bowl. Set aside.

Preheat the oven to 350 degrees F (175 degrees C). Lightly spray a fluted tube pan (such as Bundt®) with cooking spray.

Combine brown sugar, applesauce, coconut oil, and butter for the coffee cake in a large bowl. Mix with a spatula until butter is almost completely mixed in, with some chunks remaining. Mix in yogurt, sour cream, and 1 teaspoon baking soda. Add all-purpose flour, whole wheat flour, eggs, vanilla, baking powder, remaining 1 teaspoon baking soda, and salt; stir until batter is well mixed and a light brown color. Stir in raisins until evenly distributed in the batter; batter will be thick.

Scoop 1/2 of the batter into the prepared pan, smoothing it out evenly so it is flat. Sprinkle with 1/2 of the pecan topping. Repeat with remaining batter and pecan topping.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, 45 to 48 minutes. Cool on a wire rack for 5 minutes. Invert onto a cooling rack and then flip carefully so the sugary pecan-topped side remains on top. Serve warm.