According to wikionary, Satisfied, saturated and sad all come from the same latin root, meaning enough.
It's interesting to think about the evolution of the world for enough to three distinct tones: happy (satisfied), unhappy (sad) and what feels kinda technical/objective to me (saturated).

Moreover, sad reminds me of how we feel after a full meal, which we call in Brazilian (jokingly) "post plate depression".
#etimology
https://en.m.wiktionary.org/wiki/Reconstruction:Proto-Germanic/sadaz