Preheat air fryer to 325°. Place artichokes and olives in a food processor; cover and pulse until finely chopped. Unfold 1 pastry sheet on a lightly floured surface; spread half the cream cheese over half the pastry. Top with half the artichoke mixture. Sprinkle with half the Parmesan cheese. Fold plain half over filling; press gently to seal., Repeat with remaining pastry, cream cheese, artichoke mixture and Parmesan cheese. Whisk egg and water; brush over tops. Sprinkle with sesame seeds. Cut each rectangle into sixteen 3/4-in.-wide strips. Twist each strip several times., In batches, arrange breadsticks in a single layer on greased tray in air-fryer basket. Cook until golden brown, 12-15 minutes. Serve warm with tzatziki sauce if desired.