I think your table looks great “as is” without a rug. Your flooring is nice and contrasts enough to your table. I personally do not care for rugs under a dining table. It is easier, and more sanitary, to clean up food spills on a floor than food spills on a rug.

I think you need to do more with the top of the table versus getting one area rug. Don't keep the same runner; change it with the seasons to bring color and texture which you can't do with an area rug. Area rugs fix you to a space but when you don't have one it feels more flexible and open. I love the color of your floor and I think that's the star that can showcase an ever changing table top decor.  Have fun with it because you're bringing in black chairs, taking out the only color you have which is the artwork. You need color do it with the table.