We recessed ours. We gained 3/4" for the drywall and just under 4" for the 2x4stud so a bit more than 4" total is what we gained. Are your walls drywall or plaster & lath?

My walls are drywall. Did you put anything across the back to support the wall where the studs were removed? Someone told me you needed to put 1/2 inch mdf or something else to prevent the remaining drywall side from damage. If I could do this, I could get the refrigerator I want instead of getting a refrigerator I don't like for $1200.00 more.
I don't have too many choices as I want to get bisque. (Don't like stainless)

We didn't put anything across the back. We put a header and jack studs in to support the roof because this was a load bearing wall, but nothing across the back. The other side is our very tiny laundry room and I don't expect anyone to go crashing into that section of wall as I am the only one who is ever in that room.

We are recessing a fridge into the basement stairwell. She is concerned about dust, and connections for water and electricity. The architect is using 2x4s turned sideways with drywall.

We just removed a wall to even our kitchen/dining area. We pushed the wall in about 6 - 7". What the contractor did was fram out a whole wall and built studs around the area to recease the frig. Worked out well. Good luck. (it wasn't a supporting wall)