Wouldn't that need a second device since one can't screenshot Google Authenticator?
Correct.
Or take a picture of the phone screen, say with a webcam.
Nice. You know I hadn't once bothered to click the "big plus button" UI element. I headed straight for the "three dots" UI element > Settings > Import/Export submenu, every time. Joke's on me for not exploring Aegis's interface more fully ;)