Yes, if I'm understanding your question. That sounds like a good work-around for you. I don't have enough wall space on the side wall to put a recessed cabinet, unfortunately

You can surface mount the medicine cabinets. Just make sure you specify that, so you get the model with mirrored side panels for the exposed sides.

In my previous house I had vent pipes re-routed to allow space for recessed medicine cabinets, so sometimes it can be done, but requires more time and money to accomplish.

You could do a partial recess, but then you have to figure out how to cover the unfinished/exposed side panels. You could probably fill it in with some cut down wood trim pieces and paint to match the wall color.

My recessed 24x48 Robern medicine cabinets in current house.

Chispa, it sounds like the OP is in a multifamily building, so rerouting pipes is probably not a viable option.

"I find it hard to swallow that drain pipes are installed directly behind walls."

Where else should they go? Behind the wall is better than surface mount.

My daughter put a recessed cabinet over her toilet. I believe it is about 8 inches deep which includes the door. It is recessed and has 5 inches of cabinet showing. Lots of storage, Custom made, so not cheap.

You can check for other medicine cabs over the toilet that are recessed that have a picture on the door frame (like a work of art)

Robern also sells a tall storage cabinet with a mirror that might fit in your bathroom depending on your layout.

I wonder if there is room for two tall, narrow, mirrored recessed cabinets on either side of that pipe, and a flat surface mirror in between? And I would mirror the inside doors of those cabinets, too.

You could purchase a medicine cabinet that allows for recessed + surface mounting. You could then partially recess the cabinet if you want.

EDIT - I just noticed that you linked the medicine cabinet that you are interested in purchasing. Those are nice cabinets! Kohler may have a similar style - if you can't find one, I'd talk to someone who works with custom mirrors in order to have mirror sides made that can be attached. You could also cover the sides with some thin aluminum or stainless steel sheets (typically 0.016 to 0.032 inches thick) in the finish that you want. Both are highly rust-resistant, easy to cut with tin snips, and can be easily glued or screwed to the sides for a clean, custom finish. I imagine that you could hire someone who works with metal to fabricate side covers for you (people often engage pros to fabricate metal covers for vent hoods - this seems like it would be an easier project).

I like these from Kohler. They are more expensive - however, the sides are finished to match the mirror frame + there are mirrored surfaces on back of the door and behind the shelves. They look much nicer than the less expensive ones.

Determine where you want to recess the cabinet and carefully remove the drywall. The worst thing is that you may have to relocate it a bit and patch the drywall.