I would recommend either a solid color fabric, or a very soft, subtle pattern (almost tone on tone). The fabric on the chair seats and the chair backs already have quite a bit of detail, and the wood shutters bring in some texture as well, so I think your drapes should create a simple but elegant backdrop. My favorite look for drapes are ones that are fairly close to the wall color, (could be a tone or two lighter or darker) and that are hung from as close to the ceiling as possible, ending just above the floor (floor length, but not puddled). If you have enough room on both sides of your windows, extend the rod past the width of the windows by about 10-12", so that when the drapes are open, they can hang straight down with the inner edge just meeting the window, and not actually covering it. I personally love linen drapes, but if you want a little more bling, consider an edging like a Greek key in gold, or a silk drape that has some sheen). Double or triple the panels on each side, for a full look. Here are a few looks to consider. Going with a higher contrast drape, like a blue or green from your chair fabric or art, could look quite good too, but I'd still stick with a more solid color look. Please keep us updated with what you decide to do. :-)

I'm crazy about how this gold looked with your walls - are they showing at all green? does art have a bit of yellow/gold? The ivory seemed in the rug also, and a brightener, and neutral. https://www.pier1.com/chunky-jute-trimmed-ivory-pillow/3189282.html#ct-cross-sell

I would ask for a recommendation from your HVAC contrcator.

My son watched some you tube videos and ordered some sort of vegan leather to make attached seat/back cushions for his family’s kitchen banquet. Much easier to keep clean. Maybe you could get a piece of plywood cut to fit your bench, some high density foam, and some vegan leather and staple gun yourself an easily cleanable, slide-acrossable bench cushion. It looks like the bench has a little lip around the edge which will keep the plywood back cushion in place.