In Touch you can use a facet SOP to “consolidate points” thus making the same point “house” multiple vertices and stay connected when that point moves. Many other 3d apps don’t do this and only really have vertices for each primitive. You can also prepare it in houdini in this way and output a bhclassic file. If it’s a really fine model of a small unit scale you want to pay close attention to the distance threshold or scale up then back down after the facet as things may snap to places you don’t want them to.
edit : looked at your file a bit, and it seems connected somewhat already. You probably want to post how you’re doing it in TD, as i think maybe your shader is what is pulling the vertices apart. I just tested with the height map feature of PBR, and though messy it does seem to keep most points together without the facet, tears occur where the UVs have seams i imagine which would make sense regardless of a connected points or not.