The sideboard is quite charming and could be painted to match the cabinets. But, look at the doors. They leave that awkward space on either side making things hard to reach. (Not to mention you'd have that odd 5" to dust frequently to keep the dust-bunnies from colonizing.) A built-in could be designed to suit your needs. Would you sew at it, or would you put the machine on the table? If the latter, make the cabinet counter-height or higher with a stool, which might be easier to work at. Add pencil drawers for all those little pesky things. The skirt all across the bottom, hiding shelves designed to suit your storage needs, and you are good to go. Or, you could add the elements that make the sideboard charming to your built-in, like the details at the top and base (do have a base, so your stuff isn't sitting right on the floor), and you have the look of the sideboard and the efficiency of the built-in. Love that space, so sunny and airy!

Not sure but you will be adding chairs to the table and possibly extra chairs on either side of sideboard. Should be fine. Just look At DR ON Houzz forvtegetence!

We dont have one yet, just moved to a new house. But Ive been eyeing this one for a while now. https://www.restorationhardware.com/catalog/product/product.jsp?productId=prod18890271&categoryId=cat10310014

126" - 40" = 86" which is 43" each side of table. You couldn't really squeeze anything over 12" wide in there. And that would be tight. Is there room elsewhere for you bar storage? What's in the room with the windows behind the dining area? What space is available in the kitchen? The rug is small, but you don't really need a rug in dining area. In a small room the rug can come closer to the walls. I think the table,chairs and light work fine with the built in. You are living in a house that already had it's own personality, and I don't see the need to erase it. But I wouldn't introduce a cabinet with a really different style, so if you get one try to find something simple that will get along with existing furniture.