Turn on a multi-functional pressure cooker (such as Instant Pot®) and select Saute function. Add butter and stir until melted. Add onion and saute until golden brown, about 5 minutes. Stir in rice and pour in 1 1/4 cup chicken broth or as much as needed to cover rice. Close and lock the lid. Select rice setting according to manufacturer's instructions; set timer for 12 minutes. Allow 10 to 15 minutes for pressure to build.