Bring a large pot of salted water to a boil. Add 12 ounces linguine and cook until al dente according to package directions. Before draining, reserve 1/4 cup of the pasta cooking water. Drain the pasta and set aside.
In a large skillet over medium-high heat, melt 1 tablespoon butter. Season 3/4 pound shrimp with salt and pepper. Add the shrimp in a single layer and sauté 2–3 minutes, until opaque and just cooked through. Remove the shrimp from the skillet and set aside.
Add 1 tablespoon olive oil to the same skillet and keep the heat at medium-high. Season the 1 boneless, skinless chicken breast (cut into 1/2-inch dice) with salt and pepper. Add the chicken and cook 3–4 minutes, stirring once or twice, until no longer pink in the center. Remove the chicken and set it aside with the shrimp.
Add the remaining 1 tablespoon butter to the skillet. Add 3/4 pound Andouille sausage (sliced), 1 medium diced onion, 1/2 cup diced green pepper, 1/2 cup diced red bell pepper, and 1 stalk diced celery. Cook 4–5 minutes, stirring occasionally, until the sausage is browned and the vegetables are softened.
Add 3 cloves minced garlic, 1 teaspoon paprika, 1/2 teaspoon garlic powder, 1/2 teaspoon oregano, and 1/2 teaspoon thyme. Cook about 30 seconds, stirring, until fragrant.
Stir in 1 tablespoon Worcestershire sauce, 1 cup diced tomatoes, 1 tablespoon tomato paste, and 3/4 cup chicken broth. Bring to a simmer and cook 3 minutes.
Add 1/2 cup heavy cream, stir to combine, and simmer 3 minutes to warm and slightly thicken the sauce.
Return the cooked shrimp and chicken to the skillet. Add the cooked linguine and the reserved 1/4 cup pasta cooking water. Toss or stir to combine and simmer 2–3 minutes, until everything is heated through and the pasta is coated. Taste and adjust seasoning with salt and pepper as needed.
Serve immediately, topped with the 3 sliced green onions.