You do not have the wall speace for "barn" doors. Look for a frosted glass wood door and have them made into a prehung double door unit. Visit a real local lumberyard and they will definitely have options to choose from (stay out of the box stores).

How about reusing some beautiful salvaged wooden doors. Very classy.

IMO the inside there could be really fabulous and then add doors that match your cabinets I think a pantry is just another cabinet and I always do them to match

Well if an upgrade is the goal then barn doors are not the answer. Don't waste money on the inside--it's a CLOSET after all. You probably have to stick with by fold doors but yes they can be a whole lot more attractive.

is there a reason the opening has to be so big? If you were to frame in the right-side half you would have more storage space on the inside and could do a simple pocket door, or a smaller barn door or just a regular door with the walk-in open section on the left side.