This seems to be another feature that was broken / removed by switching from Nautilus to Nemo.
It seems that I can no longer keep separate desktop icons / folders on separate monitors.
Instead, it appears to be an ''all or nothing" approach where icons are either 1. Duplicated across both screens 2. Shown only on one of the two screens or 3. Not shown at all
I would like to see the original behaviour restored where different files / icons can be dragged across different screens.