To my knowledge, no, you can’t use true non-euclidean space. However, there are two ways I can think of to simulate it.
The first way is to use a shader. This seems to be what you were asking in actuality, but it’s not true non-euclidean space. Rather, everything would exist in euclidean space, and would just appear to be non-euclidean. For example, let’s take translating euclidean to spherical space. You’d want to use a sphere instead of any actual planes in order for things to look normal, then you’d have to warp each asset such that with the offset through the translation, the mesh still looks normal. You’d then make a sphere without a collider, and make it as big as the world space is. You’d then want to write a volumetric shader which skews light such that it rotates around the center of the object. This should provide the effect you’re looking for, but it would be a pain in the neck to manage. You’d need to mess with the rotation of the character a ton, and manually make gravity. It would be tricky to work with, because all of the Unity methods still operate in euclidean space, and you’d be effectively working in spherical space.
The other way to make this effect is just to simulate it. There’s a bunch of jumping through hoops that you’d have to do, but essentially, here’s the rundown. Create a floor plane with the edges surrounded by wall planes orthogonal to the first plane with render textures on them. Attach a camera to the center of each bordering plane and slightly in front, then bind the render texture of each plane to the camera on the opposite plane. You’ll have to mess with the FOV until it looks right on them. Next, just attach a script so that if anything interactive collides with a plane, it’s transported to the opposite side. There, now you have a simulation of spherical space in euclidean space.
Now this method isn’t perfect (for example, perpendicular lines still don’t intersect), but it’s a good start. You can’t make truly non-euclidean space in an engine built for euclidean space, simple as that. Note that, as with truly spherical space, this would show the objects repeating infinitely into the distance. Anyway, hope this helps!!!
EDIT: Two extra things I thought of, the wall planes should be infinitely high, and they should actually not be planes, but rather, cubes which extend into the space you can’t enter. Just make sure to include the objects distance from the surface when determining where to teleport it.