The linked accounts could be causing the problem. The dropbox documentation is very vague about how it is supposed to work, and I can't test it.
Assuming that your library is in the "Personal" dropbox, from what I understand from the documentation things should work if you tap the "Personal" button. That is supposed to connect CC to the personal account as if the other linked accounts did not exist. At that point you should see the folders, which clearly is not happening in your case.
One point: CC will work only if the calibre library is in a subdirectory in dropbox, not in the root. In other words, the metadata.db file must not have the name /metadata.db, but instead have a name like /something/metadata.db.
I might be able to find out more from a
CC debug log. If you send me one, please remove the multipie.co.uk address.