It would be nice if the noise tool could be used to preview noise with any coordinate system. I noticed that when using the noise tool, it seems the view/transform matrix up vector is +Y, so you can only properly preview the noise you want to use in your own app if your view matrix up vector is +Y, or you make similar adjustments to the same effect

I think the easiest way to do this is to let the noise tool's view matrix rotate in any direction (I noticed it is clamped to a certain range), so you can conveniently preview your noise when for example, it depends on position output nodes with falloff intended to tweak height across the X or Z dimension.

But you could also add an option that manually changes the view matrix up vector.