I decided to research it. It doesn't appear that the furniture was first.
https://en.wikipedia.org/wiki/Study_(room)#History says:
> The study developed from the closet or cabinet of the Renaissance era. From the beginning of the 18th century onwards increased literacy at the middle-class family level led to the setting aside of closed study and library areas within larger houses."
I found a 1635 example of such a closest in "A commentary vpon the Epistles of Saint Paul to Philemon, and to the Hebrewes together with a compendious explication of the second and third Epistles of Saint Iohn." at https://llds.ling-phil.ox.ac.uk/llds/xmlui/bitstream/handle/... :
> There must be a closet, or a place to study in, that is, the chamber of our owne hearts."
https://www.etymonline.com/word/study says:
> Sense of "room furnished with books" is from late 14c.
It's unlikely that there was a specific "study" desk at that point. https://en.wikipedia.org/wiki/Desk#History says:
> Desk-style furniture appears not to have been used in classical antiquity or in other ancient centers of literate civilization in the Middle East or Far East, but there is no specific proof. Medieval illustrations show the first pieces of furniture which seem to have been designed and constructed for reading and writing. Before the invention of the movable type printing press in the 15th century, any reader was potentially a writer or publisher or both, since any book or other document had to be copied by hand. The desks were designed with slots and hooks for bookmarks and for writing implements. Since manuscript volumes were sometimes large and heavy, desks of the period usually had massive structures.
Here are some early desks:
1480 - https://en.wikipedia.org/wiki/Saint_Jerome_in_His_Study_(Ghi...
1478 - https://www.museothyssen.org/en/collection/artists/malesskir...
1500 - http://ica.themorgan.org/manuscript/page/14/77089
I don't see how they particularly inform the modern study.