This is a very fun space! Which items need to stay?

This space gives you plenty of opportunities to add built-ins along the back wall.

Keep the cats.

Eliminate the clutter of books and odd shelving by building matching bookcases on the gabled end or ends for them. Full-height, or even IKEA Billys of various heights. But matching and covering the entire wall or walls.

Clean out the files and get rid of any paperwork you don't absolutely have to keep. You might be able to move it all to document boxes on the shelves.

Put the desk where the light from the skylights is best. Perpendicular to the wall under the skylights might work, facing the LR area and the windows. That puts the bookcase behind you for papers and references.

For the "in the eaves" storage, haul it ALL out into the loft and vacuum the storage. Get rid of the stuff you were storing "just in case", outgrown clothing and tattered storage boxes. Rearrange things in there so the stuff you need most often is close to one of the hatches, and the once a year stuff is near another. All the holiday stuff, all the heavy clothing ... whatever. Put it back in labelled boxes.

Instead of a sofa bed, consider an air-bed for guests.

Bring in a comfy chair for reading, maybe placed near that railing so you can sit there and see out the windows and check on the rest of the house.

Lazy_gardens is spot on - the first step here is to get rid of as much as you can. This is a process - probably not a weekend job! You need to inventory and evaluate everything, asking yourself if you use it, and if you love it. But once you see what you REALLY need to store, it will be a lot easier to organize the space in a pleasing way.

One challenge with this kind of storage is putting things back where they were, simply because that's where they were before. Optimize your "prime real estate" - the space with the best lighting. Decide which one or two tasks will be primary for the room, and concentrate on those. Right now it's trying to be too many things, which makes the room feel unsettled instead of peaceful.