Shapes, areas of simple polygons and circles, Pythagorean theorem, volume of solids, graphing, translation, all that stuff and more that one might call “geometry”, is scattered between roughly ages 6 and 12.

I think the high school level “geometry” class—which may be the only one named such, but primary school math is full of geometry—is an atrophied organ left over from when it was still common to teach directly from Euclid, which is why it tends be about introducing proofs more than covering new abilities and techniques in geometry (though it may cover some of that, too)

No. The formal geometry class is usually age 14/15 (first or second year of high school). They should have seen a less formal treatment of geometry before then, though they may not know it.