Also, what is that type of square called? It’s apparently a thing in homes in this area. Now that I’m looking, I can’t find examples to help guide and inspire me, of course.

Is your floor tile still available? If you could match it, then with tiled floor, your options for many colors & patterns of area rugs for that dining room would be wide open. Your ceiling is interesting - have you explored lighting and color options for the layers? I would take out the wall feature - it may complement the furniture you had in this room but I think it’s limiting for doing anything in this room & to me, It’s not really interesting. If you want to keep it, I’d at least remove the three items & hang a very large, complementary colored framed art inside that rectangle.

Is the rug installed , or laying over the tile. I would shop for a rug/piece of carpet you like with a pattern incorporating your colors. Then you can decide on a color for the place on the wall. You could go ahead and remove the black hangings and paint over the rust with primer to give you a blank canvas to work from. You could also look into removing the whole framed area. If you can match the existing paint well enough you might be able to get away with just painting that one wall.

I would remove the moulding, and remove the black things, and patch up the nail holes, sand it and prime it, and paint it the same color you choose for the wall. If there is tile under that piece of carpeting, then I would remove the carpet and just use an area rug, if there is no tile under there, then I would still remove the carpet and have a hardwood floor installed into that area. I would do all this before deciding on paint.

Can you repaint the whole space? I think even a lighter beige color would work better for you. And give you a more subtle palette to work off of

Simplest solution, remove the black things and paint the whole wall the same color.

Or, remove black things and trim, fill in holes and repaint the whole wall.

Agree you should eliminate it, reno the wall and paint to match all else. Your tile may be pretty common and could be matched with new. Consider a serious cleaning of the old tile and having it all re-grouted with a grout that matches the stone color. Paint in general is selected to work with fabrics/textiles. What kind of upholstery is on your dining chairs?

Not seeing your entire space, it is hard for me to clearly judge the best options for you. I am also assuming this is your dining room, but I could be wrong. At any rate, I like your red accent, and red is a very good color to have in dining areas - which is why it is often used in restaurants and eateries. You have good instincts!

I don’t know if you could do a wall color that could be isolated to just that area. If so, I feel a grey could be dramatic - and I am generally the last person to recommend grey for wall color. But I feel like it could possibly work here, if it could be somehow isolated to that area. I don’t want you to turn your house into a grey walled house, throughout. :)

I am seeing the grey in this case as serving more along the lines of an accent for your space; accent walls, so to speak. And it may also serve to give the area more definition.