Paint the entire room all one color including the ceiling and the arch. It will make the arch disappear. Update the lights, mirrors, and hardware. These in expensive tweaks will greatly improve the space.

I think the floor is fine.

Replace the hardware with black hardware. Agree with above one color paint. The door mirrors are a LOT! Can you use window film to reduce the impact?

Also remove the small art pieces and get a larger statement place for the tub area.

Gold hardware in my opinion

In addition to some of the other changes already recommended, I would also get rid of the plantation shutters. I just don't like having "bars" on the windows.

I would do light filtering Duette shades with bottom-up/top-down option, so you can have privacy on the lower part and actually have an unobstructed view of the outside for the rest of the window. Like this. If no need for privacy during the day, you can have them fully open to enjoy light and views.

Please consider hiring an interior designer. You have a house that has some very unique and beautiful classic touches that will only become muddied junk if you try to use online hodgepodge advise.