Preheat the oven to 350 degrees F. Coat a 9-inch springform pan with cooking spray. Prepare and bake the cake batter in the prepared pan according to package directions for a 9-inch pan. Let cool completely in the pan and on a rack, about 1 hour.
Meanwhile, combine the gelatin with 1/4 cup water in a small microwave-safe bowl and set aside to soften, about 5 minutes. Beat the cream cheese on medium-high speed in the bowl of a stand mixer fitted with a paddle attachment (or in a large bowl if using a hand mixer) until completely smooth, about 1 minute. Scrape down the sides of the bowl. Add the confectioners' sugar, sour cream, vanilla, lemon juice, vanilla and salt and beat until incorporated and smooth, about 1 minute.
Microwave the gelatin until melted, stirring as needed, about 30 seconds. Add the gelatin to the cream cheese mixture and beat to combine, about 30 seconds. Remove 1 1/2 cups of the mixture to a medium bowl. Pour the remaining batter into the springform pan, on top of the cake, and refrigerate until slightly set, about 30 minutes.
Add the milk to the reserved batter. Spoon 2 tablespoons each of the batter into 3 small bowls. Add black and navy blue food coloring to the remaining batter in the medium bowl and stir until incorporated and the color of a dark night sky (about 1/4 teaspoon each). Remove 2 tablespoons of dark sky batter to a small bowl.
Add the yellow food coloring to one of the uncolored batters and stir until incorporated and neon yellow. Add the pink food coloring to another uncolored batter and stir until incorporated and neon pink. Add the orange food coloring to the last uncolored batter and stir until incorporated and neon orange.
Pour the dark sky batter from the medium bowl on the cheesecake and spread evenly to coat.
To make fireworks: Use a small spoon to drop a small pool of one of the colored batters on the cheesecake. On top of the colored pool, add a pool of the reserved dark sky batter; add a pool of colored batter on top of that (the batters will spread and form concentric circles as you add alternating spoonfuls of color). Repeat with more sky and colored batter until you have 4 or 5 colored concentric circles. Drag a long skewer from the center of each circle outward to create fireworks streaks. Repeat the process with the remaining colored batter, making some fireworks big and some small. Chill in the refrigerator until completely set, 4 hours and up to overnight. Remove from the springform pan before serving.
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