Preheat oven to 350°. In a medium bowl, combine 3 tbsp. oil, 1/4 tsp. salt, and 1 tsp. sumac. Cut pitas in half and split them horizontally. Brush all over with sumac oil. Stack, cut into 4 wedges, and arrange on 2 rimmed baking sheets.
Bake pita chips, turning once, until deep golden and crisp, 12 to 15 minutes. Let cool.
Increase oven to 450°. In bowl used for pita oil, combine 1/2 tsp. salt, 1 tsp. sumac, the lemon zest, coriander, cumin, and remaining 2 tbsp. oil. Add carrots; toss to coat. Spread evenly on 1 rimmed baking sheet. Roast carrots, stirring once, until browned at edges, 15 to 18 minutes. Let cool.
Cook butter in a medium frying pan over medium-low heat, stirring occasionally, until browned, 5 to 8 minutes. All at once, add raisins, hazelnuts, 1/2 tsp. thyme, and remaining 1/2 tsp. sumac. Cook, stirring, until raisins puff, 45 to 60 seconds. Let cool.
In a bowl, combine yogurt, 1/4 tsp. salt, and remaining 1/2 tsp. thyme.
Spread yogurt on a platter. In another bowl, toss carrots with nut mixture and parsley. Spoon over yogurt and serve with chips. Add more salt to taste.
*Find at gourmet grocery stores and at worldspice.com.
Make ahead: Through step 5, up to 5 hours; chill yogurt and carrots separately. Bring carrots to room temperature, about 1 1/4 hours, before continuing.