Turn the pressure cooker on to the sauté function and add 2 tablespoons of the oil to the pot. Add the sausage, sauté until lightly browned on the outside, 3 to 4 minutes then transfer to a plate and set aside.
Add the remaining tablespoon of oil to the pot along with the onion. Sauté until softened, 2 to 4 minutes, then add the garlic and cook just until fragrant, 1 minute longer.
Shut off the sauté function on the pressure cooker.
Stir in the tomatoes, oregano and 1 cup of the chicken broth, then scatter the spaghetti into the pot in a spoke pattern to prevent it from sticking together.
Add up to 3/4 cup of additional chicken broth to bring the level of liquid nearly up to the top of the spaghetti. Note: It isn't necessary to totally submerge the pasta in liquid.
Scatter the mushrooms over the spaghetti and top with the sausage and any juices that have accumulated on the plate.
Secure the lid on the cooker and set the pressure valve to the sealed position.
Program the cooker for 4 minutes on high pressure. Once the cooking is complete, allow the pressure to release naturally for 4 minutes, then open the valve to release the balance of the pressure.
Open the pot, add the tomato paste and parsley and combine well. Let sit for 5 minutes before serving.