I'm using webdav storage for my PDFs (on iOS), but every article I click on just shows "Cannot Load Document". Everything works fine on MacOS with the Zotero client.
I'm having the exact same issue. I can't really offer a solution for you, but I can tell you that I've found this to be tied to importing an article through Papership's built-in browser (whether on Mac OS or iOS). If you instead find the PDF through Safari, or some other app, and share it to Papership, things will work fine (on Mac OS just drag and drop the PDF to your Papership window, or simply use Zotero).
Of course, another option is to use Zotero's file storage, then importing through Papership's browser works fine. I'm assuming Papership is actually just triggering a bookmarklet, so that Zotero.org pulls the PDF, and Papership then downloads it from there.
All in all, the problem seems to be tied to the way Papership's built-in browser imports PDFs, since upload (of PDF to webDAV as well as the database entry at zotero.org) works fine when the PDF comes from somewhere else.