Strawberry Pocky Stick Cake

Name: Strawberry Pocky Stick Cake
Ingredients: 2 sticks (8 ounces) unsalted butter, at room temperature, plus more for greasing the pans; 3 1/2 cups all-purpose flour, plus more for flouring the pans (see Cook's Note); 2 teaspoons baking powder; 1 1/2 teaspoons baking soda; 1 teaspoon fine salt; 2 cups granulated sugar; 4 large eggs, at room temperature; 2 cups buttermilk; 1 tablespoon pure vanilla extract; 2 pounds confectioners' sugar (about 8 cups); 4 sticks (1 pound) unsalted butter, at room temperature; 1/2 cup whole milk; 1/4 teaspoon kosher salt; 1/4 teaspoon strawberry extract, optional; Four 2.47-ounce boxes strawberry cream-covered biscuit sticks, such as Pocky®; Red gel food coloring, for coloring; Confetti sprinkles, for decorating