I am trying to use a technique I learned in this [www.youtube.com] tutorial, on using a rest attribute to apply textures to a VDB growth.

I have pored over exactly what he does in the video several times and am 99% sure I am not missing any steps - this seems proven to me by the fact that I get the exact correct triplanar texture behaviour when the material is viewed though the Houdini VK viewport renderer. The problem is that when switching to Karma, the texture projection is completely different / wrong - as shown in the photos.

PS. in the video, there are no UVs used, and no rest normals - although in the process of trouble-shooting, I did try creating rest normals and applying the exact same processes as done for the rest - which has unfortunately made no difference.

This seems less like a case of the specific treatment of rest attributes and more like a shading problem - if anything was wrong with the calculations, surely it would not work perfectly in viewport? Why is this discrepancy happening only in Karma?

I am really tearing my hair out over this, so any advice would be very, very much appreciated! Thank you!

hard to tell just from the image, but your Karma image definitely looks like it's using some sort of rest attribute since it's messy, otherwise it would look like world space aligned projections, so maybe VK is the one ignoring it

try creating just default rest from P using Rest SOP and see how it looks

Looks suspiciously similar to problems you may encounter when applying deformation motion blur to attributes on mesh that has changing topology between frames...
Can you try disabling motion blur, or switch to velocity blur (via Render Geometry Settings LOP) and see if the problem persists?