In a small bowl, combine the olives, parsley, cilantro, shallot, olive oil, lemon juice, orange zest, garlic, red pepper flakes, salt, and black pepper. Let sit while preparing the fish.
Pat the branzino dry thoroughly with paper towels. Season both sides with garlic powder, salt, and black pepper, then rub lightly with olive oil.
To roast, heat the oven to 400°F/200°C. Arrange the fillets skin-side up on a parchment-lined sheet pan. Scatter the lemon and orange slices around the fish. Roast until nearly cooked through and opaque at the center, 8 to 10 minutes. Broil until the skin is crisp and lightly blistered, 1 to 2 minutes more.
To air-fry, cook the fillets at 400°F/200°C until crisp and cooked through, 7 to 8 minutes.
To pan-sear, heat a large skillet over medium heat with a thin layer of olive oil. Cook the fillets skin-side down until deeply crisp, about 3 minutes. Turn carefully and cook until the flesh flakes easily, 3 to 4 minutes longer.
Transfer the crispy branzino to a platter and spoon the citrus olive salsa over the top. Serve with the roasted citrus alongside.