Just tested, the last problems with wrong clipping seem to be fixed in VTK 9.3 (latest release candidate rc2)!
The above example program runs nicely, except for a few errors in the console:
vtkOpenGLFramebufferObj:356 ERR| vtkOpenGLFramebufferObject (000001419E3E3D40): failed at glDeleteFramebuffers 16 OpenGL errors detected
Edit - Correction: The near plane clipping problem is not yet fully fixed, but it has improved somewhat - the volume in the example code above is shown correct until the HMD gets close to the volume borders. When very close or in the volume, the clipping plane is quite far away from the eyes (nearly on the opposite side of the volume, but at least not in the wrong direction anymore).