Besides those "strange" depictions of animals and humans, there is also plenty of medieval art that is still regarded as highly beautiful today (admittedly especially once we're leaning towards the Renaissance).
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)
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