How to do with a shallow closet

You usually start with the current opening (if finished) and pick a standard door size, add in for gaps (3 gaps: Left hinge, right hinge and center).

Typical gap sizes would be 1/8 on either side and 3/16 in the middle

If the opening is currently drywall, the corner beads would be removed and a wooden jamb is installed left, top and bottom. Casing molding is installed over the jamb to cover the gap between the jamb and the original opening.

Roller catches at the top center are nice, because there is not a usual single door strike plate

You have a choice of door handles (which will need wider stiles) or cabinet pulls,

Why not build your closet wall along the dotted line, but end it at the inset near the window. Build a short return wall to the edge of the inset.

Then on the short wall to the left of the window, build in a bookshelf ceiling to floor that is slightly less deep than the closet wall (inset about 2-3") and just short of the window trim. You could also build a companion bookshelf on the right side of the window to make it look symmetrical.

The small step back from the edge of the closet to the bookcase would likely look planned rather than makeshift. You also could have the edge of the closet rounded as it moves back to the bookshelves. There are pre-made curved edges, called bullnoses, available for plasterboard that would make it fairly simple.