Ensure the Instant Pot has the stainless steel insert in place.
Press the Saute setting and heat the olive oil in the insert until shimmering.
Add the chopped onion and minced garlic and saute until the onion is nearly translucent, about 3–4 minutes.
Stir in the dried Italian seasoning and oregano.
Add the Italian sausage (casings removed) and cook, breaking it up with a wooden spoon, until no longer pink and browned bits form on the bottom, about 5 minutes.
Press Cancel/Off. Add 1/4 cup water and scrape the browned bits from the bottom to deglaze the pot.
Add the ziti and 2 cups water, stirring to combine and distribute the pasta evenly.
Pour the diced tomatoes with their juices over the pasta, then add the tomato paste and crushed tomatoes. Do not stir.
Close the lid and set the valve to Sealing. Select Manual (or Pressure Cook) and set the timer to 6 minutes.
When the cook time ends, press Cancel/Off and quickly release the pressure by switching the valve to Venting. Carefully open the lid.
Stir in the shredded mozzarella and ricotta until the sauce is creamy and the cheese is melted.
Season to taste with kosher salt and black pepper, then serve.
