Earlier quoted context omitted.
I thought most keyboards at least ask for Full Access, though may not necessarily mandate it: https://techcrunch.com/2014/10/04/everything-you-need-to-kno... I was never sure what "Full Access" meant, other than keyboard data (including keystroke recording if the dev wanted it) going forward. But surely it doesn't mean everything , as in access to keyboard-non-related data (user photos, etc).?
The documentation for that is here: https://developer.apple.com/library/content/documentation/Ge... The gist of it is that requesting "full access" allows them to access the internet and some other bits automatically, but they need to ask for further permissions for photos, location, contacts, etc.
Yep, it's not everything, but "full access" gets a scary name because when you give your keyboard a network connection it can easily log and send off all of your passwords. Very few things on iOS have that level of access.