Gosh, your woodwork is gorgeous! I wouldn’t be inclined to cover it either. I’d do wide slat plantation shutters. They would fit inside your window frames and give excellent privacy at night, plus provide a bit of architectural interest to your actual windows which look like black holes without muntins. Typically I love long, full silk drapes in a dining room...but I feel it would be guilding the lily in your room! :) I’d get an amazing rug and a stellar piece of art for the non-window wall and call it a day. Beautiful architecture!

I would go with curtain panels.

Or bamboo shades?

Roman shades would work too

I brought some transitional decor in room