Closet door too short
Even though someone is using it as a closet, that is an &quot;alcove&quot;, so it was not built to have a door. So you will have fitment issue no matter what you do; the crown molding at the top is a problem, the baseboard on the left side it another, where a sliding door would slide to is a problem, etc. etc. etc.
Were it me, I would make a new top header extending down just below that crown molding and add some right side trim to give a straight edge for it to close against, then use a &quot;barn door&quot; external track system on the wall to the right. Ignore the color and style of this door, but here is an example of the type of slide system.