Turn on a multi-functional pressure cooker (such as Instant Pot) and select Saute function. Heat oil; add mushrooms, rice, and shallot, allowing the shallot and mushrooms to saute and the rice to toast just slightly, about 5 minutes. Turn off the Saute function. Stir in broth and wine. Close and lock the lid.
Select high pressure according to manufacturer's instructions; set timer for 23 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure using the natural-release method according to manufacturer's instructions for 12 minutes. Release any remaining pressure carefully using the quick-release method, about 5 minutes. Unlock and remove the lid.
Season with salt and pepper. Stir and serve immediately.