I think round for the table would be a better choice of shape since you have that bay . Is there a reason for 6 seats all the time? I think maybe you could check out the Saarinen table in an oval but I would need to see a to scale plan of that area you could do the same table in a round too. I have no idea of the color of the cabinets but they seem to work well in the space , is it important to know the actual stain color? Do you use that door in the bay? If so then IMO no way to get an oval in there and 6 seats

Rug really depends if you are wanting a neutral or some color. First finalize living room - rug, art, accessories and then look for a dining set that complements its overall look. Hard to recommend an actual set, but just look to tie living and dining, choose the appropriate size and consider seating needs.

Medium brown. I have lots of medium brown oak wood pieces of furniture and staircase in my home, and they all blend well with my other eclectic pieces.

Table/floor are fine and once you add chairs especially, it will feel more be broken up. Suggest buying chairs first, as they can add up quickly and are harder to find/decide on than a rug. If you have young children, I’d skip upholstered chairs and solidly made ones can be quite expensive. Some ideas below, but have to suit your kitchen as well, but I like the Studio McGee ones. https://studio-mcgee.com/fall-dining-refresh-with-studio-mcgee-for-target/?ssp_iabi=1677093199257