Pat the chicken thighs completely dry with paper towels. Season both sides with kosher salt, black pepper, and garlic powder.
In a large bowl, whisk ½ cup of the pesto with the olive oil and lemon juice until loose. Reserve the remaining 3 tablespoons of pesto separately.
Add the chicken to the bowl and turn with tongs until fully coated. Rest 10 minutes if time allows.
Preheat the air fryer to 380°F for 3 minutes.
Arrange the thighs in a single layer with space between them, skin side up. Cook boneless thighs 16–18 minutes total, flipping at 9 minutes. Cook bone-in thighs 22–26 minutes total, flipping at 15 minutes.
In the final 2 minutes, brush the reserved pesto over the chicken and sprinkle with Parmesan if using.
Check the temperature at the thickest part: 165°F for boneless, 175–180°F for bone-in.
Rest 5 minutes, garnish with fresh basil, and serve.