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If the rotation axis was arbitary I wouldn't try to do the same in Inkscape, it would be much easier to use a 3D program - no matter the construction has been known hundreds of years as a part of engineering.

The rotated red face would need totally different transformation, so it's constructed indirectly. I skip more general proceedings. As I said, I would use a 3D program to make arbitary rotations with a couple of clicks.

  In the next image the faces are redrawn with the pen as closed shapes and colored to white and red:

The corners of the rotated version will fit only in some lucky cases to the original grid - like just in your case the z-edge could be recycled and that made the construction simple.

If the rotation axis was arbitary I wouldn't try to do the same in Inkscape, it would be much easier to use a 3D program (see NOTE1) - no matter the construction has been known hundreds of years as a part of engineering.

The rotated red face would need totally different transformation, so it's constructed indirectly. I skip more general proceedings. In the next image the faces are redrawn with the pen as closed shapes and colored to white and red:

The corners of the rotated version will fit only in some lucky cases to the original grid - like just in your case the z-edge could be recycled and that made the construction simple.

NOTE1: The next image is a screenshot from a simple 3d CAD program.

Drawing one box with certain dimensions and text is about as complex as making your original box in the grid. But all rotated copies took only a few seconds each. BTW. I switched the projection from isometric to a perspective projection, because for some reason the rotated boxes started soon to look distorted in isometric projection. There's no imaging error, it's a property of human vision.

There's no easy way to transform the already drawn box to the new rotation. It's possible, but in practice you must retract the isometric projection, rotate and then convert again to the isometric projection. As well you can draw a new box.

There's no easy way to transform the already drawn box to the new rotation. It's possible if one knows and understands 3D projection math and how it can be used in Inkscape. Without that knowledge you do better by drawing a new box. I'll follow the latter route.

In the next image there's the needed versions:

The corners of the rotated version will fit only in some lucky cases to the original grid - like just in your case the z-edge could be recycled.

The next image contains the needed versions:

The corners of the rotated version will fit only in some lucky cases to the original grid - like just in your case the z-edge could be recycled and that made the construction simple.