On a 6-quart Instant Pot, select More/High Sauté. Add 2 tablespoons of oil and heat until shimmering. Add the mushrooms and ½ teaspoon salt, then cook, stirring occasionally, until well browned and most of the liquid released by the mushrooms has evaporated, 6 to 8 minutes. Transfer to a small bowl and set aside. With the pot still on More/High Sauté, add the remaining 2 tablespoons oil and the onion. Cook, stirring occasionally, until lightly browned, 5 to 7 minutes. Stir in the garlic and cook until fragrant, about 30 seconds. Add the farro, 2 teaspoons salt and ¾ teaspoon pepper, stirring to coat the grains with oil. Add the wine and cook, scraping up any browned bits, until most of the liquid evaporates, 1 to 2 minutes. Add 3 cups water, then distribute the farro mixture in an even layer.