Baked Saffron Yogurt Rice with Chicken (Tahcheen-e Morgh)

Name: Baked Saffron Yogurt Rice with Chicken (Tahcheen-e Morgh)
Cuisine: Middle Eastern
Ingredients: 3 cups extra-long white basmati rice (1 lb. 4 oz.); 1⁄4 cup plus 2 Tbsp. kosher salt, divided, plus more as needed; 1⁄4 tsp. saffron, lightly ground between your fingers, plus more for sprinkling; 3 tbsp. extra-virgin olive oil; 1 large yellow onion, halved and sliced ¼-inch-thick; 4 medium garlic cloves, finely chopped (1 Tbsp.); 10 boneless, skinless chicken thighs (2 lb. 3 oz.), halved; 1⁄4 tsp. freshly ground black pepper; 1⁄4 cup fresh lemon juice; 1 cup plain whole-milk Greek yogurt; 1 large egg; 5 tbsp. unsalted butter, divided; 1 tbsp. unsalted butter; 1⁄2 cup dried barberries, picked, soaked in cold water for 15 minutes, then drained (or substitute finely chopped dried cranberries); 1 tsp. sugar (omit if using cranberries); 1⁄3 cup raw pistachios, coarsely chopped