the goal was no visible fasteners! The matching shelves I had done were overly complicated with dados, etc, so these were very simple, with the shelves attached to the backing board on the wall using countersunk screws, which was also how the vertical supports were attached from the bottom of each shelf. Then there are pin nails on the top of the vertical supports to stabilize them, but they’re pretty much invisible.
The whole thing is then pocket screwed to the wall under a couple of the shelves, and I used pocket screws on the bottom support since it holds the whole thing up.