It sounds like your content folders aren’t defined correctly. Can you go to Edit > Preferences > Content Library > Content Directory Manager, expand the 3 sections (DAZ Studio Format, Poser Format, Other Formats) and post a screenshot?
.obj files should not appear at all in the interface (unless you have folders for .obj which haven’t been put in Poser or DS format). So if you’re seeing .obj files in the Unassigned category, it means you have something defined as “Other Formats”.
ETA: Sorry, missed the screenshot first time. The entry under “Other Formats” should be removed, that will likely solve your problem.
I’m just going to follow this thread. I would dearly LOVE to categorize all of my content (there’s TONS of it) using metadata, so hopefully I’ll figure out at least the basics by following the conversation :D