I think the first question is why the soft constraint gets such different results from the hard constraint. Yet the result from the soft constraint doesn’t seem in any way sensitive to how hard the constraint is.
I don’t know why 0.001 * ncat is the magic scale. That’s why I suggested posting here. I was hoping @anon75146577 or @mitzimorris or @avehtari would jump in. It’s related to the spatial ICAR model soft smoothing. I have to imagine it has to be set in balance to the parameter scales, which seem to be roughly on the unit scale here.