I had a linen closet built into a bathroom, and the carpenter made the doors and drawers overlay instead of inset like the photo I showed him. Can this be changed easily?
Not easily not. The drawer fronts will have to be redone completely for size and either the glides will have to be moved back or the drawer cut down so that it's not so deep.
Ditto. Inset requires much more precision apparently so that is why it costs more . . .
It depends; there are many "ifs"
If the faceframe is presentable.
If the drawer box is separate from the face.
If he used Blum Tandem glides, or better.
If there is at least another inch of clearance at the back of the drawer box.
So lets say those conditions are all met, you will need to procure the proper Blum inset mount clips, then install the drawer boxes on them and trim the drawer face to fit the opening in the faceframe.
If some other conditions are extant, then more work would be required.
Whether or not they can easily be changed shouldn't be the question. If he didn't build the doors and drawers to your specifications (inset), he should do them over if you are unhappy with overlay, regardless of how "easy" it is. I know if I asked for inset, I wouldn't necessarily settle for overlay. Completely different look and price point.
This shouldn't be a retrofit at all. He should build you a new cabinet. And yes, part of the reason is that it's really difficult to retrofit. But the main reason should be that it isn't what you asked for.
I agree with SM.
Lots of variables, but I will say, yes, it can be done.. Anything can be done..
You dont need a new cabinet, either..