Heat olive oil in a nonstick skillet over medium-high heat. Add red onion and cook, stirring occasionally, until tender, about 2 minutes. Add spinach, cover, and cook until wilted, about 90 seconds. Stir in marinara sauce and chicken breast.

Preheat an air fryer to 325°F (165°C) according to the manufacturer's instructions.

Divide pizza dough into 4 equal pieces. Roll each piece into a 6-inch circle on a lightly floured work surface. Spread 1/4 of the spinach mixture over the bottom half of each circle. Top with shredded mozzarella cheese. Fold dough over filling to form a half-moon shape and crimp edges to seal. Spray generously with cooking spray.