Have a decent lamp with bright globe to place on desk so you have an alternative to canned overhead lighting.

Seam tape, mud, paint.

Is this an actual room with a door? If so, what is the light in the hallway like? If there is good light outside of the door, I'd install a glass paneled door to borrow light from in there and then paint the walls a nice white. If the hallway has no good light, it'd embrace the darkness and paint the walls, ceiling, and trim all the same dark color.

Have a dimmable overhead light fixture installed and use 3000k bubls. Have a good desk lamp too. Get a shaggy cozy floor rug.

Do you only work sitting at a desk or do you also like to work in a comfy chair with a laptop too? I like to work in a cozy chair and had an office this size. I put the desk on the short wall with back to the door. And I put a nice cozy arm chair with small footprint in room too. I had a small side table type ottoman that I kept against the wall but would pullout to put my feet up on.

Ikea sells wall light panels. Some people use them to simulate windows. Might be an idea.

consider all the things you NEED and simplify a plan. Use the best finishes and keep it simple.

I like the above by Lyn.

Can we see how this space relates to the rest of the house?

It's already cozy, but it's not nice. It's also not an office, it's a closet. I could never work in a space with no natural light. Having said that, Lyn's pic suggests a good starting point.