So my question is, was the initial Goya drawing that fooled Kat also a plant by The Protagonist just to establish the toxic relationship between her and Sator?
You will notice other names and events from the film on the Sator Square, including ROTAS, OPERA and the films title Tenet.
Kat mentions that first drawing was sold by a dealer named Arepo.
This may seem like another high class art dealer with a fancy name, but Arepo is actually connected to the film via the Sator Square, a famous latin palindrome.