Cook the linguine according to package directions until al dente; drain and keep warm.
Heat the oil in a cast iron pan or large skillet over medium heat.
Season the chicken strips with 1/2 teaspoon salt and 1/4 teaspoon pepper.
Add the chicken to the skillet and cook, turning as needed, until seared on both sides and cooked through, about 5–7 minutes.
Sprinkle the Cajun or Adobo seasoning, basil, garlic powder, and optional smoked paprika over the cooked chicken and stir to coat.
Reduce heat to low and stir in the heavy whipping cream and shredded Parmesan; cook 2–3 minutes, stirring, until the sauce is warmed and slightly thickened.
Toss the warm linguine with the chicken and Alfredo sauce in a bowl or large skillet so the pasta is evenly coated.
Serve topped with additional Parmesan, chopped green onions, and drained sun-dried tomatoes if using.