Preheat oven to 350 degrees F (175 degrees C). Grease an 8-inch square baking pan with cooking spray.
Place shredded carrots in a microwave-safe bowl. Cover and cook in the microwave until slightly softened, about 3 minutes.
Combine eggs, white sugar, and 1/2 cup sucralose sweetener in a large bowl; beat with an electric mixer until thick and creamy. Add canola oil, applesauce, cinnamon, baking powder, baking soda, and salt; beat until well blended.
Fold carrots and pineapple into the bowl until well mixed. Add flour and xanthan gum; mix batter until no floury streaks remain. Scrape batter into the prepared pan using a rubber spatula.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 35 to 45 minutes. Transfer to a wire rack to cool completely, at least 20 minutes.
Combine Neufchatel cheese, confectioners' sugar, 1/2 cup sucralose sweetener, cream cheese, and buttery spread in a large bowl; beat with an electric mixer until frosting is light and fluffy.