How to rotate wood ring?

Can you try to re create your project and have the auto unwrap on with the options:

I get this for a cube:

If it does not work, you can use the geometry mask to hide some parts of the mesh and apply a first time the wood, and for the other parts the wood in another layer and rotate the texutre like this:

for the geometry mask:

of course your mesh should have submeshes or UDIMs.

You could also of course split in different Textures Set.

You can also use ID maps to do that.