You already have carpet, so a rug isn't really needed.

Is there a reason the bookcases are not centered on the wall? If you want to add drapes, I'm afraid it will be too close in that corner. Or are you planning to replace the blinds?

there are a ton of options. what is your style?

Though I'm not sure how they will look with the wood wall.

Wood wall makes it a bit harder

You can go in any number of directions.

I like the the idea of something like this:

https://www.roomvo.com/share/o6jafm

Or maybe this:

https://www.roomvo.com/share/lixsg2

Are you sure you want a rug on carpeting? Do you want a guest chair? Would you consider an animal skin under desk?

Just example I could grab and put in room.

I plugged that rug in but would prefer irregular edging. I have a friend that got one from a local seller very cheap and great size. You can check those sources too.

I would size rug to keep walkway thru room clear of additional rug.

Here it is with the wood wall

I'd say it's pretty traditional. Here is link

Not sure it looks the greatest with the wood wall though.