Hanging clothes require 24" to hang straight (not at a diagonal). So your 44" width is too narrow for 2 rows of clothes since you would need 48" plus room to stand between the clothes to see them. I would put 2 full clothes rods going side to side since you seem to have mostly shirts. Get narrow hangers so you can hang almost everything. Add cubbies to the side for folded clothes.

I would hire a closet company to come in and make a plan for you based specifically on your needs. They are not as expensive as many think they are and are wonderful at their jobs.

I'd use those hanging fabric storage shelves where I show the gray area. They might stick over the door opening a big since they're usually 12" deep and your wall space there is only 12", but it will probably be OK functionally. Attach them to the ceiling since you have no clothes bar there.

Command hooks on the wall in that space might also be very useful and easy to put up if you don't need shelves on both sides.

Either remove the third rod from one side or reconfigure it so that the clothes rods run from side to side. An electrician can add lighting. Out of season clothes can be folded and kept in boxes in the way back if you choose a side-to-side configuration.