I would be interested in this as well, but I don't think New Horizons dreams work the same way. The 3DS probably wrote the dream save over your save for memory resource purposes. I doubt the switch would need to do something like that, so we would need to find where this data is stored and how to dump it. If we did figure this out, it would probably be just the map file which we would need to inject into the save with NHSE. I doubt the dreams download the whole save file like on the 3DS.