The term Papessa is Italian and Papesse is French; English is Popess.
I cannot find it recorded earlier than about 1440 in any vernacular language. Before
this date, all the sources are Latin, and refer to Pope Joan. The
Latin form is Papissa, which enters the language around 1250, in the first written account of Pope Joan.|
In the vernacular languages, suitably, the word has a much broader range of meaning than "Papissa Joanna" - from the burlesque to the sacred. They show that the term is a natural and simple substantive - the feminine form of "pope" -, and that therefore the term "Papesse" by itself can shed no light on a potential historical referent to the card.
I have only found the following four from the 15th century -
1. Pope Joan, 1440 (French)
Martin le Franc wrote "Le Champion des Dames", including a section defending Pope Joan (Jeanne la Papesse).
2. Mystery play, 1450 (French)
A text from around 1450 containing the "Mystery of Saint Bernard de Menthon".
At lines 1869-70, the Fool says -
My Mariocte would be popess".
(Si j'estoy le pape de Romme,
This early entry shows the word "papesse" in the vernacular being used in a logical way, and in a logical context - it is the feminine of "pope", in a satirical or ribald context. It is natural to assume that using a feminine form of "pape" would in itself seem to imply satire or ribaldry.
3. Pope's sister, mid-fifteenth century (Italian)
The next vernacular use I have found seems to be "Palazzo delle Papesse" (Palace of the Popesses) the nickname of Palazzo Piccolomini, Caterina Piccolomini's Palace in Siena, begun in 1460.
Caterina was the sister of Aeneas Silvio Piccolomini, who became Pope Pius II in 1458, which (according to everything I have read) explains the name. I can't find much about her, but she does not seem to have been a notorious woman, so it does not seem pointedly satirical, much less ribald. Thus, leaving aside some questions, such as when did it get the name, why is "papesse" plural, etc., it is clear that this particular use of the term "papessa" is merely gently ironic.
Coincidentally, it was in Siena's Duomo that a representation of Papa Joanne VIII, depicted and labelled "Femina", was supposed to have been displayed, along with all the other Popes up to that time.
And interestingly also, it was Aneas Silvio Piccolomini in 1451 (before he became Pope) who is credited with showing the first slight glimmer of doubt about the historicity of Pope Joan.
4. Virgin Mary or Church as Bride of Christ, late 15th century (Catalan)
In the late 15th century, the Catalan Abbess Isabel de Villena (1430- 1490) wrote the "Vita Christi", which was printed for the first time in 1497. Chapter 238 has a hymn to either the Church or the Virgin Mary, which contains the lines -
to whom our Lord has committed great treasures".
(Vos, Senyora, sou la gran Papessa a qui
nostre Senyor ha comanat los grans tresors)
These four little instances of the vernacular term "papesse" span 50 years of the 15th century and they span the range of possible uses of the word "papesse" and "papessa". I think this range of contexts shows that the title of the card alone cannot shed much light on the meaning of the image. For that we must look to the pack and the game itself, and contemporary images of the same figure.