See.. what I find interesting and frustrating is how inconsistant the iconography really is!
What I'd really like is to say that there are two popes (either both male or one male and one female). And that the difference is that one of them holds a book, and the other one gives a blessing. Or that one of them holds a book, and one of them holds a staff. Or that one of them holds a book, and one of them wears a triple crown. None of this is "true"
For the iconography, we have a mixture of many things. Single Key, Double Keys, Triple Cross, Single Cross, Crossier, Book, One Attendant, Two Attendants.
I look at the Mantagna.. and we see "The Pope" shown with a book and keys. Maybe a triple crown. So what this says is that the book and the keys can be said to represent "a pope". Fine. Interestingly, note the chair with the animal heads in the Mantagna and the chair in the first image I found of Augustine. Not saying it means anything.. just interesting connection.
I'd like to be able to say.. *in the Tarot*.. Book = Popess Card and/or Doctor of Canon Law. Most of the images of the "figure with the book" are identified with the Popess. The Cary-Sheet, and Budapest, and Bologna we are not certain. IF we want to say that the full figure in the Cary Sheet is actually a Popess.. (she has the Crossier like the Budapest, she has the book), and the other partial figure is the Pope... and we want to say that the figure with the Crossier is the Popess in the Budapest. Then that opens up.. to me.. the option that the Figure on the Charles VI may be a "Popess" card.. which is showing a Doctor of Canon Law.
But the crossier itself isn't clear enough. If we want to say that the figure with the crossier in the Cary Sheet is the Pope, that conflicts with the Budapest... unless we want to say that the figure in the Budapest with the crossier is the Pope. If so, that means that the figure in the Budapest with the shield with two keys held by two attendants is the Popess.
You mention that the image you have of Augustine shows One Key and a book. That matchs the Geofroy and Paris Popess. It also matches the Charles VI card, unless the Charles VI shows two keys.
Lots of questions here. We have several early cards with a Single Cross (bologna and Visconti), we have several with a triple cross (Conver, Geofroy, Paris), and we have several with a Crossier (Budapest, Cary-Sheet, Vieville, Noblet, and Dodal)