I believe it would be best to minimize air flow by building the alcove with 2x6 material (which is wider than the 3.25” load center) that would isolate the space behind the load center from the rest of the stud cavity. See diagram below.
Thanks Frank. It is from Google Sketchup. Greet tool but it takes some time to learn. Easier than tools like AutoCad though.
The local inspector is not to keen on working with homeowners despite having paid for permits. The inspector did send a diagram of an alcove in a 2x4 fire rated wall which showes the blocking/supports the full width of the 2x4 (not posting diagram as it appears to be from a copyrighted source). Since the diagram is with a 2x4 wall there is no mention of space between the other side of the wall’s drywall and the back of the alcove.
The opposite side of the wall to the alcove is drywalled. It is removed in the diagrams for visibility.