Set the Instant Pot to Sauté (high). Add 1 tablespoon olive oil and heat until shimmering.
Season the chicken strips with 1/2 teaspoon salt, 1 teaspoon oregano, 1/4 teaspoon garlic powder, and 1/2 teaspoon black pepper; toss to coat evenly.
Sear the chicken in the hot pot 1–2 minutes per side until lightly golden and slightly reduced in size; remove to a plate.
Add the remaining 1 teaspoon olive oil to the pot, then sauté the minced garlic, chopped asparagus, sliced mushrooms, and chopped sun-dried tomatoes about 45 seconds until garlic is fragrant and veggies begin to soften.
Return the seared chicken to the pot, add the pasta, 1 1/2 cups water, 1/2 cup cream, and 1 teaspoon salt; stir to combine and ensure pasta is mostly submerged.
Cancel Sauté. Close and seal the lid. Set the pressure cooker to HIGH for 5 minutes (suitable for spirals, bowties, penne, and similar shapes).
When cooking finishes, perform a quick release according to your machine's instructions. Open the lid carefully.
Stir in 1/4 cup minced fresh basil, lemon zest, and 1 cup grated Parmesan. Season with red chili flakes and freshly grated black pepper to taste. Serve immediately.