Does your list mean Qty.3 Cable boxes, Qty 3 Rokus...etc?

Putting AV gear in that kind of cabinet is always a nightmare. Even the best/most stable closet systems fail after a while. The good news is that i dont see any amps or AVRs in the list so you aren't dealing with the weight i usually have to deal with.

I hate slide out racks but you absolutely have to do it. Otherwise you will deal with a nightmare every time you service the system. Racks are also a great way to say "dont put your underwear and wallet on this shelf".

I would build a 3/4" plywood box that perfectly fits the 36X21X33 opening. A glued and screwed solid box. Mount that box to the studs and each side of the shelf opening. Then mount your rack base to the plywood box. I would even bolt the back rails of the base to the plywood box.