For dressing:
Combine sumac with soaking liquid, 3 tablespoons lemon juice, garlic, salt, 2 teaspoons vinegar, and dried mint in a small bowl. Gradually add oil, whisking constantly, until well blended.
For salad:
Place pita pieces in a medium bowl; pour oil over and toss to coat. Season pita to taste with salt.
Mix tomatoes, cucumber, onions, salad, herbs in a large bowl. Add 3/4 of dressing; toss to coat, add more dressing if needed. Season with salt. Add pita; toss once. Sprinkle sumac.