Kovall built in
This built in is most similar to my design, with the shelves attached to the side wall and open on the TV side. There is also a grasscloth back. I don't envision the need to have lighting below the shelves. The wall with the built in includes a soffit at the top - larger than yours - but of course no cove.
This shows the base cabinet deeper than the shelves. Also shows flat front doors (we would add hardware) and cabinets on the taller side like those I designed. This also shows how the protruding base cabinets can feel more furniture-like compared to a built in tucked between walls. I also want you to note that the top, although stained, is deeper than the base cabinet, not flush. That's a nice detail I incorporated into your design.