Preheat the oven to 350 degrees F (175 degrees C).
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.
Melt butter in a large saucepan over medium heat. Add onion; cook and stir until tender, about 5 minutes. Stir in all three condensed soups and bring to a simmer. Stir in about 1/2 of the Cheddar cheese and cook until velvety, about 5 minutes. Stir in chicken, half-and-half, pimentos, wine, mushrooms, parsley, and steak sauce; cook until hot.
While the sauce is cooking, bring a large pot of lightly salted water to a boil. Add angel hair and cook, stirring occasionally, until tender yet firm to the bite, 4 to 5 minutes.
Drain pasta and place into a large baking dish. Pour soup mixture over pasta and toss until well coated. Scatter remaining Cheddar cheese over top and sprinkle with paprika.
Bake in the preheated oven until liquid is bubbling, about 45 minutes.