Turn on a multi-functional pressure cooker (such as Instant Pot®) and select Saute function. Heat oil in the pot and add mushrooms, onion, and garlic. Saute until mushrooms are tender and onions are translucent, about 5 minutes. Push Cancel. Transfer the mushroom mixture to a paper towel-lined plate and set aside. Clean the inside of the pot when it is cool enough to handle.
Whisk eggs and heavy cream together in a medium bowl. Stir in spinach, Parmesan cheese, salt, pepper, and garlic powder until well blended. Add the mushroom mixture and stir until well combined.
Pour 1 cup water into the pot and place a steamer rack trivet in the bottom.
Spray a souffle dish or other heat-proof dish with nonstick cooking spray. Pour egg mixture into the prepared dish and cover loosely with foil. Place the dish on top of the trivet.
Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 30 minutes. Allow 6 to 7 minutes for pressure to build.
Release pressure using the natural-release method according to manufacturer's instructions, for 10 minutes. Release remaining pressure carefully using the quick-release method, about 5 minutes. Unlock and remove the lid. Remove foil from the frittata and pour off any excess liquid before slicing and serving.