If needed, slice each chicken breast in half horizontally or place between parchment/plastic and pound to about 1/2-inch thickness.
Combine the flour, Italian seasoning, garlic powder, and kosher salt in a gallon-sized resealable bag; add the chicken, seal, and shake to coat evenly.
Set the Instant Pot to Sauté and add 2 tablespoons olive oil. When hot, brown the chicken 2–3 minutes per side, working in 1–2 batches so pieces don’t overcrowd. Remove browned chicken to a plate.
Pour the chicken broth into the pot and scrape up any browned bits from the bottom with a wooden spoon.
Stir in the marinara sauce, then nestle the browned chicken pieces into the sauce so they are mostly covered.
Cancel Sauté, secure the lid, set to Manual/High pressure, and cook for 8 minutes.
Allow a natural pressure release for 10 minutes, then carefully quick-release any remaining pressure and remove the lid.
Sprinkle the shredded mozzarella over the chicken, replace the lid for 2–3 minutes until the cheese melts.
Serve the chicken breasts over cooked spaghetti and spoon extra sauce from the pot over the pasta.