If you're taking that much trouble, you will probably choose your stock with care. I'd advise that!
If your vertical piece with dovetail splits, there goes the support for the shelf.
A couple of years back, I made one, mainly from scrap, to take all our cast iron cookware, etc. It's quite deep to take the bigger pans, and it's got diagonal braces underneath instead of brackets (they go into angled tenons top + bottom), and I added a batten at the back under the shelf, like the one in the picture. That pulls the back of the shelf into the wall tightly, and effectively stops any excess weight turning into a splitting-away force.
At a guess, the shelf in your picture is screwed down onto the batten, out of sight. The batten can be screwed firmly to the wall, and if it's flexible enough, it will hide wall contours too (they're rarely flat), otherwise you either have to scribe the back of the shelf, or have an unsightly varying gap, as viewed from underneath. It's much easier to fix the batten first to a levelled line, than to try to get two or more brackets all aligned and square.
Also, if it's going to be a high shelf, consider a lipping that projects above very slightly, to catch things rolling off. All these designs depend on the wall being vertical - they very often aren't, and having a small lip reduces the need to pack things out (which looks ugly unless you're very careful). I guess you could leave the vertical thick, and plane it to match any lean in the wall, but that would be "fun"!
Personally, I wouldn't dado the shelf - it weakens it especially at the ends (the wall batten helps this though). Either screw down from above or set in dowels to locate the shelf on the brackets - screwing down is a lot easier. We don't have a 'minimalist" kitchen like your picture - ours is full of clutter. So I have to assume anything/everything fixed to a wall will get overloaded at some point, and design accordingly.
E.
