Toss the squash, zucchini, and onion with olive oil, salt, and pepper. Air fry at 375°F (190°C) for 8–10 minutes to soften slightly.
Mix sour cream, shredded cheese, eggs, garlic powder, thyme, and paprika until smooth.
Fold in the pre-cooked squash and zucchini mixture until evenly coated.
Combine Panko, Parmesan, and melted butter in a small bowl.
Grease a heat-safe baking dish that fits in your air fryer. Pour in the veggie mixture and sprinkle the breadcrumb topping evenly over it.
Air fry at 350°F (175°C) for 12–15 minutes, or until bubbling and golden on top.
Let the casserole rest for 5 minutes before serving.