I find that the sync of the “Starred” folder is often unreliable and I find that a significant number of papers that are starred in Paperpile don’t show up in the corresponding Google Drive folder. Unstarring and re-starring the paper usually resolves this.
I have a suspicion that possibly papers that are starred before the PDF is downloaded are not being synced, but I’m not sure about that. In any case, the correct behaviour should be that a starred paper that has a PDF added (or changed) later should be updated on Google Drive automatically.