Turn Instant Pot on to SAUTEE function. Chop ¼ onion, ½ carrot, ½ celery stalk, 1 c mushrooms, and rosemary leaves from 2 sprigs of rosemary. Pour 1 tablespoon olive oil into Instant Pop bowl, followed by chopped vegetables, ¼ teaspoon salt. Cook until onions are translucent and mushrooms shrink, about 5-8 minutes.
Once vegetables are soft, add 1 c water, 1 teaspoon chicken bouillon paste, ⅓ c wild rice, and frozen chicken tender to vegetables. Stir and cover with lid. Set vent to SEALING and set to cook on MULTIGRAIN for 25 minutes.
When done cooking, set vent to VENTING for quick release and remove lid once steam is released. Stir soup. In a small bowl, add ¼ c milk and 1 tablespoon flour. Stir with spoon or fork. Add to soup to thicken it.
Dish soup into bowl and top with parsley as a garnish if desired. Add salt and pepper to taste. Enjoy