Combine the smoked paprika, garlic powder, onion powder, kosher salt, and black pepper in a small bowl. Reserve 1 tablespoon for the sauce.
Preheat the air fryer to 375°F for 3–5 minutes and lightly spray the basket.
Pat the chicken thighs completely dry with paper towels. Rub the remaining seasoning over the chicken, working some under the skin.
Arrange the thighs skin side up in a single layer, without crowding. Cook for 18–20 minutes, flipping halfway, until the internal temperature reaches at least 165°F. Do not add sauce yet.
While the chicken cooks, whisk together the ketchup, balsamic vinegar, brown sugar, olive oil, and the reserved 1 tablespoon of dry rub.
Brush the cooked thighs generously with barbecue sauce. Return to the air fryer skin side up and cook 2–3 minutes, until the glaze caramelizes. Watch closely — the sugar burns quickly.
Rest 5 minutes before serving.