It's built in, just hidden. First add it: Settings > Control Center > tap the green + next to Screen Recording. Now swipe down from the top-right corner to open Control Center and tap the round record icon (a dot inside a circle). It gives a 3-second countdown, then records everything on screen. Tap the red status bar > Stop to finish, and the video saves to Photos. It captures app audio automatically, and if you long-press the record button you can turn on the Microphone to narrate too.