Melt butter in a skillet and cook onion until soft and translucent, about 5 minutes. Remove from skillet and set aside.

Preheat the oven to 350 degrees F (175 degrees C).

Combine Neufchatel cheese, chicken broth, pesto, dry Italian salad dressing, garlic powder, black pepper, Italian seasoning, and red pepper flakes in a bowl and beat using an electric mixer until well combined. Stir in spinach and sauteed onions. Gently fold in tomatoes and basil. Transfer mixture into a casserole dish.

Season chicken with salt and pepper and place on top of spinach mixture in the dish.

Bake in the preheated oven until chicken is no longer pink in the center and the juices run clear, 20 to 30 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).

Remove chicken from casserole dish, top with mozzarella cheese, and microwave until cheese is melted, about 1 minute. Serve chicken topped with spinach mixture.