I tried the dae solution with enabling the v3 scheduler, checking the database, and forcing a full one-way upload sync. After that I added a card and got the same error: “Error - Please use the Check Database function, then sync again. If problems persist, please force a full sync in the preferences screen.”
I tried more than this today, including re-installing Anki mobile on my iPhone. The problem seems to lie with adding a card only. The review functionality seems to work.
I tried ordinary upload, ordinary download, full upload, and full download. Nothing resolves the issue.
One last tidbit: I can add a card in the MacOS version of Anki and upload it, and when I synchronize with the iOS version, no error. It seems to be specifically creating new Anki cards on iOS version.