Not to diminish Wittgenstein’s influence, quite the contrary, but I for one first heard about the idea of a “private language” while reading the works of Wilhelm von Humboldt [1], written around the 1830s (so about a century before Wittgenstein). I remember Humboldt saying something along the lines of “at the limit, we each speak our own, private language”. I read his work in translation, as I don’t speak German, so I cannot tell how much of a direct overlap there is between von Humboldt and Wittgenstein in terms of the nomenclature they were both using.
[1] https://en.m.wikipedia.org/wiki/Wilhelm_von_Humboldt