That's not quite correct... GA now allows you to create a single "QR Code" on screen that you're supposed to scan with Google Authenticator on a "new" device and it will import all your codes for you... but there is no option to "save" that QR code and screenshot is disabled within the app. As far as I can tell, the idea is that you go directly from GA on Device 1 to "authenticator app" on Device 2 etc... Aegis does seem to be able to read and import this single QR Code tho.
Great, thanks for clarifying that. I have never tested their latest "backup" method, I guess I memorized it wrongly. The method you described is safer than having to save a unique unencrypted file that some users would surely end up losing, misplacing, or leaking to third parties. From your and NeuroticFish's answer I can conclude that you are both using multiple 2FA apps. Is it possible to have authentication codes of the same site across two or more 2FA apps at the same time?