The bugbear with rectangle tables as opposed to round IMO is that seats are spread out therefore it’s a nuisance when all seats are full and the passing of food, condiments, drinks etc.

Round is more sociable. Each person can reach their own items.

The room has a high level of squares and rectangles through the furniture style, the rug, the decorative glass on the right hand wall and the patio doors opposite so a rectangular table would certainly carry this theme on although a round table would pick up the roundness of the woodburner beautifully. Not really answered the question but maybe food for thought [pardon the pun!]

I prefer an oval shape. Eliminates square corners, looks a bit softer but still spacious for family gatherings.

It is said that the table should follow the room's shape but in your case it takes too much space, because it feels narrow. If you don't have a large family constantly eating there I recommend the round one or, even better, to keep the shape scheme, a small square one.

I don't think it matters as I think round, rectangular or oval would work but whichever shape you go for needs to be centred to the island ……

The rectangle table you have shown has curved corners and looks great so I would stick with that. If you decided to have a round take I would prefer that centred as well which may mean not having the unit along the wall.

table not take