Add the chopped onion, carrots, baby bella mushrooms, and butter to the Instant Pot. Turn the Instant Pot to sauté mode and cook stirring frequently and scraping the bottom to remove any stuck on bits until the onions turn clear, about 5 minutes.
Add the chicken breasts, chicken broth, rice and seasoning packet from the rice and stir well to make sure the liquid is distributed to the bottom of the pot and nothing is stuck on. Set on Manual- high pressure to cook for 8 minutes. Once it is done cooking, let the pressure release naturally for 5 minutes, then quick release any remaining pressure.
Remove the chicken carefully (it will be hot) from the soup and chop it into small bites. Stir the chicken back into the soup and then slowly add in the heavy cream while stirring constantly. Stir in 1/2 tsp salt, then add up to an additional 1/2 tsp to taste.
Serve as is, or if you prefer a thicker broth, remove 1 cup of liquid from the soup and slowly mix it into 1 tbsp cornstarch. Once combined, stir the cornstarch mixture back into the soup, mix well, and replace the lid on the Instant Pot and let set for 10 minutes. Once set, stir well, serve, and enjoy!