In a medium bowl, mix cream cheese, goat cheese, garlic, lemon zest, ¼ teaspoon salt, and a few grinds of pepper.
Lightly coat an air-fryer basket with cooking spray. Place spinach in basket. Cook at 400°, tossing halfway through, until spinach is wilted, about 4 minutes (some leaves may start to dry out; that’s okay). Add spinach and artichokes to cheese mixture and stir to combine.
Using a sharp knife, make a pocket in each chicken breast, being careful not to cut all the way through. Stuff pockets with spinach mixture. Season outside of chicken with chili powder, ¾ teaspoon salt, and ¼ teaspoon pepper. Arrange chicken in air-fryer basket. Cook at 350°, turning halfway through, until an instant-read thermometer inserted into thickest part registers 165°, 16 to 20 minutes.
