Add tomatoes and remaining 1 tablespoon oil to skillet; cook, undisturbed, until blistered, about 4 minutes. Add green beans, garlic, capers, and oregano; cook until fragrant, about 1 minute. Sprinkle with remaining 1/2 teaspoon each salt and pepper. Stir in white wine. Place charred onions on top of tomato mixture; nestle chicken into tomato mixture.