A clset needs to be 2' deep tis is areach in closet and honestly I would remove the wall on that door wall and frame in for a nice Pax system from Ikea tons better storage and all easily reached .The door from what you show only serves the clast so do what I suggested for a perfec closet

Looks like my wonderful 1920s closets!! at least mine are 32” deep. most people widen to double door around here - not perfect but helps. Removing as patricia said would be highly practical too and use the doors it would look nice.

If the open bedroom door would block another closet door from opening, close the bedroom door. and open it when you are done with the closet. That is exactly the situation I grew up with. Sheesh, what is wrong with the builder? Just widen the doorway to accommodate a second door. If there is some reason that the closet and bedroom doors can’t swing into each other, you could do bypass sliding doors on the closet. or change the side the bedroom door hinges on from right to left.

@bpath 's ideas will solve the two problems. Install full bypass doors AND change the bedroom door swing. Mirrored or painted closet doors are both good options.

Edited to add: The door hinges would be on the other side of the door, but it would still open into the bedroom.

Bypass doors are the answer. Only issue could be if the closet front is load bearing.

Opening a door into a hallway is going to catch somebody unawares--and not in a good way.

@Jennifer Finan Thank you! This is the kind of wacky solution I knew was out there. :) This is clever and will fit the bill. Appreciate it!