Have you confirmed that you have the CC the build needs installed in the Mods folder in the right place? It could be that new CC you downloaded is in the wrong folder, especially if something like OneDrive has made a duplicate folder.
Alternatively, the builder may have uploaded a version that was saved with CC removed, but that isn't affecting their own version, which wasn't saved that way.
Running only a furniture batch fix in Sims 4 Studio shouldn't break anything at all. Not sure how it can.
NOTE: I'm away and likely completely offline after this until Tuesday.