This problem (saving a changed project file to NAS) has been reported before, but, so far as I know, no-one has got to the bottom of it. What is clear though is that it isn’t a Shotcut problem per se.
EDIT: I suspect that the Synology DDS thinks that the original project file is still open, hence the rename (mv) will fail. But the file must be closed since otherwise all filesystems, including locally-mounted ones would fail.