Preheat oven to 375 degrees F (190 degrees C). Line a rimmed sheet pan with parchment paper.
Whisk together flour, white sugar, baking powder, salt, and cinnamon in a large bowl.
Whisk together milk, cooled butter, eggs, and vanilla extract in a second bowl. Add to flour mixture and carefully mix together without overmixing. Fold in 1/2 cup blueberries.
Pour batter onto the prepared sheet pan and smooth into a 1/2-inch layer with a spatula. Sprinkle remaining 1/2 cup blueberries over 1/3 of the batter, strawberries onto the middle 1/3, and banana slices over the last 1/3. Drizzle banana slices with caramel topping. Sprinkle everything with turbinado sugar.
Bake in the preheated oven until edges are just turning golden brown, about 20 minutes. Remove from the oven, let cool for at least 10 minutes, and slice into squares.
