Hey @dsurka,
One thing to be aware of is that whenever you author scene description in Houdini, you are doing so on an anonymous (in-memory) layer. Since anonymous layers do not have real paths, they can’t meaningfully be used to anchor relative paths. For this reason whenever you use a Load Layer for Editing node, Houdini will make all of the relative paths in the layer absolute. Similarly, the default behavior of the USD ROP has the “Use Relative Paths” output processor enabled which attempts to convert any absolute paths to relative when writing the layer(s) to disk. I mention this because, as far as I can tell, you should only author relative paths in Houdini using an output processor.
With regards to resolving UDIM paths specifically, I think that the thread you linked is probably the best reference:
USD itself doesn’t have a UDIM resolver so the empty string is due to failed resolution.
The one thing I would add is that USD 23.05 introduced UsdShadeUdimUtils which includes some utilities for handling UDIMs that you may find helpful.