I am not a fan of round rugs, but in this case round seems to be the direction that works best in this room. Doesn't have to be this design.

Between the two shapes am liking the round rug better but as Beverly posted you might be able to find a better pattern.

IMO a nice oiece of art on the wall and then a rug if you must . I do not like rugs in eating spaces so no rug would be my choice . You have been looking for a rug for a long time maybe no rug is the answer

such a charming spot 😍 i like the round rug with the blue and all the plates on the wall

Not a pro... but I like either one, and both are o.k. with chair fabric.