Halve cheese sticks into 24 pieces; place on parchment-lined baking sheet and freeze at least 1 hour.
Set out three shallow bowls: flour; eggs; breadcrumbs mixed with Parmesan, garlic powder, oregano, and salt.
Dredge frozen cheese in flour, dip in egg, coat in crumbs, then repeat egg and crumbs for double coating.
Return to sheet; freeze another 30 minutes to hold coating during cooking.
Spray air fryer basket; arrange frozen sticks in single layer without touching. Lightly spray tops.
Air fry at 390°F for 6-8 minutes until golden brown and crispy, in batches if needed; serve immediately with warm marinara.