If you have time, you can saute the onion, celery and carrot for 3 to 5 minutes in a drizzle of oil before adding the rest of the ingredients.
You can use water instead of chicken broth (or a combination of the two) but the soup won't be quite as flavorful. You'll definitely need to add more salt after the soup is cooked to help boost the flavor.
If you want the rice to have a firmer texture, you have to cook the rice for a shorter amount of time. To do this, follow the instructions for this recipe but don't add the rice. Once the soup is done, take out the cooked chicken breasts and add the rice. Cook the soup again for 3 minutes. Then, add the chopped chicken breast back into the soup.
This recipe was tested in a 6-quart instant pot.