The depth available is smaller than the wall suggests. A nominal two-by-four stud measures about 38 by 89mm, and 12.7mm of drywall gives a little over 100mm from the finished face to the sheathing behind. A recessed cabinet with a 100mm body therefore just fits, with its frame standing proud. Anything deeper has two honest answers: fur the wall out on the room side so the recess sits in the new build-out, or work in a wall framed from two-by-six. Width behaves the same way — studs at 400mm on centre leave roughly 360mm clear, and going wider means cutting a stud and heading the opening.
An exterior wall is the wrong wall, and there is no mild version of that. A recess displaces the insulation and interrupts the vapour barrier at exactly the point where the most humid room in the house meets the coldest surface available to it. Condensation then forms inside the cabinet, in still air, where nothing dries. Where the location genuinely cannot move, the wall is furred out on the inside and the recess lives entirely within that new depth, leaving insulation and barrier continuous behind it. The same reasoning rules out a wall between a dwelling and an attached garage, or one shared with a neighbouring unit, because those assemblies are doing a fire separation job a hole would cancel.
Then the bay has to be proved empty. The wall behind a toilet is the one everybody wants and the one most likely to be the wet wall, with a 75 to 100mm stack and its vent filling the cavity. Switch loops, a circuit passing through, a fan duct and a heating run all compete for the same space. A scanner finds studs dependably and pipework poorly, so the only reliable step before committing is a small exploratory opening cut at the intended position and looked into. Once the bay is clear, the recess is framed with a sill and a head plate and the cabinet fixed to those rather than to drywall.