Prepare the Cake: Preheat oven to 350°F. Generously coat a 9- x 13-inch baking pan with cooking spray. Line bottom of baking pan with parchment paper; coat paper with cooking spray. Beat butter with a stand mixer fitted with a paddle attachment on medium speed until creamy, about 1 minute. Gradually add sugar, beating until light and fluffy, about 2 minutes. Add eggs 1 at a time, beating until just blended after each addition.

Whisk together flour, baking powder, and salt in a bowl. Add flour mixture to butter mixture alternately with milk, beginning and ending with flour mixture, beating on low speed until just blended after each addition. Stir in vanilla. Pour batter into prepared baking pan.

Bake in preheated oven until a wooden pick inserted in center of Cake comes out clean, 30 to 40 minutes. Transfer Cake in baking pan to a wire rack; let cool 10 minutes. Invert Cake onto wire rack; let cool completely, about 1 hour.

Prepare the Fillings: Stir together 1/2 teaspoon each of the cornstarch and water in a small bowl; set aside. Stir together blueberries, 1/3 cup of the sugar, 1 1/2 tablespoons of the orange juice, 1 1/2 tablespoons of the lemon juice, and 1/8 teaspoon of the salt in a medium saucepan. Bring mixture to a simmer over medium, stirring constantly. Continue simmering, stirring occasionally, until sugar dissolves, about 5 minutes. Stir in cornstarch-water mixture; simmer, stirring constantly, until mixture thickens slightly, 30 seconds to 1 minute. Remove from heat; let cool 15 minutes. Process mixture using an immersion blender until smooth, about 30 seconds. (Alternatively, transfer mixture to a blender, and blend until smooth.) Pour mixture into a bowl; cover and chill until cold, about 1 hour. Meanwhile, repeat procedure with remaining cornstarch, water, sugar, orange juice, lemon juice, and salt, using chopped strawberries in place of the blueberries.

Assemble the Cake: Place Cake on a serving plate. Using a 1/4-inch-wide wooden dowel or the round handle of a wooden spoon, poke holes spaced 1 inch apart over the entire Cake surface, poking at least three-quarters of the way through the Cake, but not poking all the way to the bottom. Spoon blueberry and strawberry Fillings alternately in lengthwise rows over Cake surface, being sure to fill all holes. Chill, uncovered, 1 hour.

Prepare the Frosting: Beat mascarpone cheese, vanilla, and 1/4 cup powdered of the sugar with a stand mixer fitted with a whisk attachment on medium speed until just combined, about 30 seconds. Add heavy cream; beat on medium speed until foamy, about 30 seconds. Increase speed to medium-high; gradually add remaining 1/4 cup powdered sugar, beating until stiff peaks form, about 1 minute, 30 seconds. (Do not overbeat.)

Spread Frosting evenly around sides of chilled Cake. Dollop remaining Frosting onto top of Cake, carefully spreading over top. Garnish with fresh blueberries and strawberries.