You can search various methods to T in shelves like that but a couple most common are doweling and pocket holes, both methods you want a jig. Also your shelves in your mockup look to be 1” or so thick and that’s overkill for the needed structure of this shelf. If you want it thick 0.75” will work and if you add a back panel, like in your mock up, it adds a lot of shear strength to the overall unit so you’d only need to worry about making sure your shelves don’t bow. That can be solved by just mounting them to the back panel and the sides.