Those are custom built into the wall with Soss Hinges or similar most likely. Framed opening for starters when the house was framed possibly as well.

This woman built a "medicine cabinet" box and shoved it into the wall. I suppose you could build a box with a door flush with the surrounding drywall. You'd use, I suppose, a j-bead to finish the edges of the drywall that surrounds the box, hinges that would allow the door to swing out (so it wouldn't hit the drywall), and push latches.

But how would you finish the door? Paint it like the surrounding drywall? After awhile it would be dirty with fingerprints.

But here's the real question: What's the point?

I did this for a linen closet it my last place by using J-bead in the door opening, making a flush door and building a stop that covered the rest of the rough framing in the door opening. I did not use Soss hinges for this I used heavy duty cabinet hinges on it made for flush doors.

In this house we had a spot where the framing was wider over the in the wall tank for a toilet in an adjacent bathroom, so it was a perfect spot for a medicine cabinet. However it was half exposed, half hidden behind the bathroom door when open, because it is a small bathroom. We built a box that fit in, and it was actually mudded in with zip strips, I think they were called and put a flush door on this as well, with cabinet hinges.

Both have pulls on them. Linen door had an almost invisible edge pull, medicine cabinet has a regular pull on it. That bathroom is papered so the paper continues over the door.

The point of doing this was to have as least obtrusive linen closet door because of it's location, and the same for the medicine cabinet. I would not use touch latches because that Will get dirty. But with the pulls we have the doors did not get marked at all. I don't know, I don't touch anything with dirty hands except the sink hardware so I don't think that it's dirt you would have to worry about with a touch latch, but oils from your fingers. Also the touch latches have an issue with getting out of flush with use. Best to use a simple hinge and an unobtrusive piece of hardware.

For what it's worth, my closet door are all either lacquered the same color as the walls or covered with wallpaper and hinged with pivots or soss-type, and by being careful with opening and closing them with the edge pulls they have stayed clean for years. The papered doors were done about 7-8 years ago and don't have a mark on them.

Millworkman is right in that some of this has to be planned in the framing stages. I did a number of recessed things and some dimensions based on tile dimensions and it all had to be addressed from the start with how the framing was done.

There are things like this:

https://ezconcept.com/products/access-panels/

But the doors may not really that suitable as a cabinet/daily access kinda thing, unless you can put a discreet pull on it.

And of course that's just the door. One must construct the medicine cabinet/box that sits behind the door.

Also this works better in a 2x6 wall rather than 2x4 since the door is recessed.

Right now this sort of thing is not an "off the shelf" product. It's either partly or fully custom.