I also have a problem with this feature. I was able to drag and drop items into the My Publications folder in the desktop version of Zotero a few months ago, but I can no longer do so. When I drag an item from my library (not just a PDF, but any bibliography entry), I check the checkbox in the popup window and click the Add to My Publications button. However, when the popup window closes, the item is not there. I have tried this dozens of times.
Can you provide a Debug ID for a drag attempt?