This recipe is written for an electric pressure cooker.  You could absolutely do this on the stove, using your best judgement for time.

Mix xanthan gum with water to try to blend.  I have found the simplest and best way to do this is to put a few tablespoons of water and 1/2 to 1 teaspoon of the xanthan gum in one of those very small round ziplock containers.  Pop the top on, and shake it like crazy.  Set aside.

If you are using a pressure cooker, you do not need to pre-soak your dried mushrooms!  If you make this recipe on the stove, you should soak the mushrooms.

Put all ingredients except eggs and xanthan gum into the inner liner of your Instant Pot or pressure cooker.  Cook using high pressure for 18 minutes.

Allow the pot to release pressure naturally for 10 minutes, and then release remaining pressure.
Turn pot on Sauté to allow the soup to stay hot.  Poor the xanthan gum and water mix, now gel, into pot through strainer if chunks form and if chunks bother you. Stir.

If necessary, remove the mushrooms, and slice them thinly, and put them back into the soup.

Slowly pour in the eggs. Mix three times around with chopsticks. Cover the pot and let the eggs cook slowly in the broth for a minute, and then serve.  If you do not eat eggs or don’t have any, this soup is equally delicious without them.  We generally make the soup without the eggs, freeze, and then add eggs if we think about it when we are reheating.