[thaumasiotes]

> 2D hyperbolic geometry (not possible to create in 3 dimensions, completely foreign to us)

Foreign to us, yes. It's perfectly possible to represent a hyperbolic paraboloid in three dimensions.

https://mathworld.wolfram.com/HyperbolicParaboloid.html

> so I don't think it is a 'display' issue at all.

...you just complained that moving around a sphere should count as non-Euclidean if it's displayed inconveniently, but not if it's displayed conveniently. But you don't think that's a display issue?

[zenorogue]

The hyperbolic paraboloid is not an isometric embedding of the hyperbolic plane H2 in Euclidean space E3, because it does not have constant negative Gaussian curvature.

In general it is impossible to have an isometric embedding of H2 in E3, although it is possible to have isometric embeddings of fragments of H2.