The wall unit reminds me of a recent challenge, where we had to mount a TV in pretty much the same wall unit.
The cabinet guys are focused on a visually clean installation and spaced the entire unit about 3/4" off the wall to ensure the front lined up perfectly. The large flat 1/4" wood surface we were to hang the TV from was 1/2" to 3/4" off the actual wall. It was quite a challenge to get that back piece to support the TV!
A good answer is easier with a clear question giving the make and model of everything. "The biggest problem in communication is the illusion that it has taken place." -- G. “Bernie” Shaw