Preheat the oven to 375°F (190°C) and lightly coat a 9x13-inch baking dish with cooking spray.
In a large mixing bowl, combine the shredded chicken, alfredo sauce, Greek yogurt, cream cheese, garlic powder, Italian seasoning, ½ cup of mozzarella cheese, and ¼ cup of Parmesan cheese. Mix until well blended.
Spread the chicken mixture evenly across the bottom of the prepared baking dish.
Arrange the frozen tater tots in a single layer over the chicken mixture.
Cover the dish with aluminum foil and bake for 20 minutes.
Remove the foil, sprinkle the remaining mozzarella and Parmesan cheeses over the tater tots, and bake uncovered for another 10 minutes or until the tater tots are golden and crispy.
Let the bake cool for 5 minutes. Garnish with fresh parsley if desired.