Mix yogurt, garlic, lemon zest, and 2 tsp. lemon juice in a medium bowl; season with salt. Set yogurt sauce aside. Mix black pepper, coriander, cumin, paprika, cinnamon, turmeric, and cayenne in a small bowl. Heat 2 Tbsp. butter and 1 Tbsp. oil in a large skillet over medium. As soon as butter is melted, add half of spice mixture and cook, stirring, until fragrant, about 30 seconds. Add half of turkey meat and toss to coat. Transfer to a large bowl. Repeat with remaining 2 Tbsp. butter, 1 Tbsp. oil, spice mixture, and turkey meat. Add remaining 1 tsp. lemon juice to turkey mixture and toss to combine. Toss onion, cucumbers, carrot, radishes, and vinegar in a large bowl to combine. Add herbs, season with salt, and gently toss again. Cut 1″ off top of each pita and stuff back into pocket, nudging it all the way to the bottom. Spread some of the yogurt sauce inside each pita without tearing sides and fill with turkey and vegetable mixture. Serve with hot sauce and remaining yogurt sauce.