If needed, slice each chicken breast in half horizontally or place between parchment/plastic and pound to 1/2-inch thickness so pieces are thin and uniform.
Rub the chicken with 1 tablespoon of the olive oil to coat.
Place the flour, Italian seasoning, garlic powder, and kosher salt into a gallon-sized resealable bag and shake to combine.
Add the chicken to the bag, seal, and shake until each piece is evenly coated with the seasoned flour mixture.
Set the Instant Pot to Sauté and add the remaining 2 tablespoons olive oil. When hot, brown the chicken 2–3 minutes per side, working in batches if needed; remove browned chicken to a plate.
Pour the chicken broth into the Instant Pot and scrape up any browned bits from the bottom with a wooden spoon.
Stir in the marinara sauce, return the browned chicken to the pot, and spoon sauce over the pieces so they are mostly covered.
Cancel Sauté, seal the lid, and cook on Manual/High pressure for 8 minutes.
Allow a natural pressure release for 10 minutes, then quick-release any remaining pressure and carefully open the lid.
Sprinkle the shredded mozzarella over the chicken, replace the lid for 1–2 minutes to let the cheese melt, then serve over cooked spaghetti.
