I was taught in school that Perspective was invented in the Renaissance, and before that all art was flat. This is obviously not true to anyone who's studied greecian art beyond a pop-culture level, but that's the level most people have.

It does seem to have waxed and waned; going in and out of popularity to the point of being a lost art multiple times. Wikipedia doesn't go so far as to divide it into eras, but given the time gaps, it's possible that there were multiple "inventions" of perspective in the sense of formalized techniques and pedagogy. https://en.m.wikipedia.org/wiki/Perspective_(graphical)

As far as I know, the earliest known example demonstrating accurate perspective dates from the Renaissance.

That doesn't mean everything was flat. Other projections were used instead of perspective to create an illusion of depth. Indeed, we still sometimes use them today, like for isometric games. There were also some works that show elements of perspective prior to the Renaissance, but afaik, none that converge perfectly across the work

i was also taught this in school, despite it being bizarrely obviously wrong?

It's a popular meme in education just like the idea of barter being some pre-currency "natural state" of exchange which also falls apart under scrutiny.