There are multiple geometries though, they don't have to describe the real world. In mathematics you are free to base your geometry on whatever axioms you want, whether they are realistic or not. I'd say the question of which geometry applies in the real world is more a question for physicists (or cosmologists, today).

This is a very late-XIX century development. Geometry used to be an integral part of physics, vide Newton's Principia.

Wondering if Euclid’s parallel postulate was independent goes back millennia though. And that’s like the key ingredient for multiple geometries.

No, it's trying to prove that Euclid's parallel postulate can be derived from other axioms is what goes back millennia. People were certain it's a) true, b) necessary consequence of other axioms. Gauss was probably the first to consider the possibility that it may be false; others at best tried reductio ad absurdum, arrived to some wildly unusual theorems, decided those were absurd enough to demonstrate the truth of the fifth postulate, and went back to trying to derive it.

It's either true as an axiom or true as derived from other axioms and/or theorems. In neither case does latching onto Euclid's other common notions/postulates/theorems as the selection it must be proved true from make sense as a 1.5kya long task.

I think there must have been a sense that it was true only as an axiom. Proving it from other axioms/theorems was then a goal to secure it's truth "further". But you'd only attempt that if you thought there was something questionable in the first place.

> But you'd only attempt that if you thought there was something questionable in the first place.

No, that's not the only reason. Come on, people actually wrote why they tried to prove it in their commentaries on Euclid's Elements.

For example, some people found that this postulate, compared with the first four, is not really that self-evident and also has a sudden jump in the complexity of its formulation. That's why some courses on geometry replaced it with something different (but equivalent), like "the sum of angles of any triangle is 180 degrees", or "for a line and a point not on it, there is exactly one line parallel to it that passes through that point", or "there are triangles with arbitrary large areas", etc.

The real world determines which geometry applies. That's the crucial difference. Sometimes physicists use mathematical reasoning to figure things out that map onto the world and later observation validates their reasoning. But observation can also invalidate, and then physicists have to go back to the drawing board or devise new experiments.