Preheat the oven to 375°F (190°C). Place the pita pieces in a mixing bowl and add the olive oil, za’atar, sumac, and salt. Toss until the pita is evenly coated.
Spread the pita pieces in a single layer on a baking sheet. Bake for 12-14 minutes until crisp and lightly browned, flipping the pieces once during baking for even browning. Transfer the pita chips to a cooling rack or plate and allow them to cool completely.
Place the romaine, red cabbage, radicchio, cucumbers, tomatoes, radishes, pomegranate seeds, red onion, parsley, mint, and dill in a large serving bowl.
In a separate bowl, combine the olive oil, lemon juice, pomegranate molasses, garlic, sumac, salt, and black pepper. Whisk until the dressing is thoroughly mixed.
Pour the dressing over the salad and toss until the vegetables and herbs are evenly coated.
Fold in the pita chips immediately before serving.