I use Free File Sync to backup my library to a Portable Drive and move it between Laptop and Desktop and have never had a problem. I don't use syncthing at all.
I would recommend always closing Calibre before running any sync tool. I would think that syncthing is trying to modify metadata.db while calibre is working with it. Do you see the error while calibre is open or is calibre open in more than one location at the same time.
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