SOLVED:
tl;dr - use the diskette icon in the HLOD browser to save the assets. “Save all” command which formerly worked for saving HLODs and their data - doesn’t work as of UE 5.3-5.4
Long story:
It seems Epic Games changed the way HLODs are stored inside the project.
Epic started packing hlods into a single proxy file, which was not the case formerly. And, since all of the meshes, materials, and textures no longer show in content browser - the Save All command doesn’t apply to them anymore.
What you actually have to do now - is to explicitly :man-facepalming: :woman-facepalming: push the diskette icon in the HLOD editor. And this is the only way that the baking result will get saved into the proxy file… Found this by mere accident today. Couldn’t wrap my head around this problem.
Hope this helps some1 with similar issue.