Forgot to mention I’d like to keep flooring as it is new - everything else I’m open to suggestions

You have cool colors here. If you want to add colors, I like to keep a room in the same cool colors when you start off with them. Adding a taupe (a gray-brown) will warm things up a bit. You can put that on the walls and ceiling. SW 6071 Popular Gray if you want to lighten things up. SW 6072 Versatile Gray if you want your space to be more cosy. SW 6073 Perfect Gray if you want even more cosy. Have an overall plan for your interior design. For ideas - in top search box write in "cool colors in great room in photos". When it is all done, it will look beautiful!

Gray overload!
I would square off the arches. Then I would look for a large Oriental style or other patterned area rug to hold all the living room furniture: a rug @13’x18’ holds two sofas, two upholstered chairs and all the necessary tables in our house. If the rug has some gray in it, it will relate to the flooring. Then select another color from the rug for the walls, some furniture, draperies.
Art and accessories will add your personal style.

I would square off the arches but IMO that flooring is doing the home NO favors. It's grey overload, and the faux grey wood is super busy looking. It's going to be hard to work with. It's also clashing with the more traditional arches. If you got new flooring the arches probably wouldn't stick out as much.

Gray everywhere. That’s a much worse problem than arches. Gotta do something. If the gray floor is new, then everything else that is gray—which is everything—has to change, or at least as much of it as you can.

Everything is so grey looking it looks as if you posted the photos in mono. Bad photos or is this how it really looks?
I would get rid of the beams on the ceiling if possible and paint that entire big room one color, ceiling and walls...and not grey. Agree with a new front door.

You say you don't like the color, so why are you set on keeping the flooring in its current form? If it's a hardwood that can be refinished, I'd absolutely get a quote on refinishing it as part of whatever you do. If it can't be refinished, I'd get a quote on replacing it. Don't let the fact that it's new be the determining factor. If the sellers (since I'm assuming they, not you, chose the grayscale palette) had told you it was 15 years old, would you be okay with replacing or refinishing it? If so, pretend it's not new and replace away. Then square the arches and paint.

I think I would consider closing in the upstairs walkway...it just shows more doorways.