In your Instant Pot, layer your ingredients in the order they are listed: shallots, garlic, chicken breasts, dried basil, dried oregano, salt, pasta, chicken stock, and pasta sauce. Do not mix. Gently spread the pasta sauce over the pasta if needed.
Set the Instant Pot lid valve to sealing and set the manual pressure for 7 minutes. Once done, quick release.
Stir in the mozzarella and parmesan until melted into the pasta or close the lid and let the leftover steam melt the cheeses.