Bring a pot of water to a boil. Cook chicken breasts in boiling water until no longer pink in the center and the juices run clear, 12 to 15 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Cut chicken into 1-inch pieces.
Bring a large pot of lightly salted water to a boil. Cook angel hair in the boiling water, stirring occasionally until cooked through but firm to the bite, 4 to 5 minutes; drain.
Melt butter in a large saucepan over medium heat. Cook and stir onion in butter until tender, about 5 minutes. Pour mushroom soup, chicken soup, and celery soup into the saucepan; stir and bring to a simmer. Add about half the Cheddar cheese; stir into the soup mixture and cook until velvety, about 5 minutes. Stir chicken, half-and-half, pimentos, wine, mushrooms, parsley, and steak sauce into the soup mix; cook until hot.
Toss angel hair pasta and soup mixture together in a large baking dish; top with remaining Cheddar cheese. Sprinkle paprika over the cheese layer.
Bake in preheated oven until the liquid is bubbling, about 45 minutes.