I learn axonometric projection in school, Z is up.
Meanwhile, Autodesk has Y up.
If you google around, axonometry also have a different representation in axes, depends from style to style.
And related to the Cartesian, there are 2 types.
Planar Cartesian, which does not really include Z, and if you scroll down you see 3D representation on Wikipedia, has Z up.
Also if you rotate your model around, X can be up.
As I said, differs for everyone's perspective, especially dev's perspective.