When thinking about barn doors and how they can be used inside the house the first thing that comes to mind is the bedroom.
Barn door inside or outside room.
On this kind of door the exterior trim is wide enough that you will still see the frame around the door despite the overlap.
It will look fine i have a larger door on a barn track will take a photo from the kitchen and post it for you.
If your barn door is the entry to a bathroom or bedroom you ll find different privacy latching solutions available from a hook and eye closure to a latch with strike plate even a decorative deadbolt.
This works on the outside but you ll need to install a recessed pull on the inside so the door clears the door jamb when it slides open.