I’m not normally a fan of round rugs, but I think it works well in your situation. And I like woven there, too.

I like the darker color of your first one.

round rug works only if you son’t add a leaf, creating an oval. Make sure rug is a flat, SMOOTH finsh and binding so chair legs don’t catch and binding doesnt curl.

Make sure the rug is large enough the chairs are completely on when pulled back to sit. At a minimum 2' wider on each side. That means at least a 9' round.