Is there any way to separate the "dining" room cabinets away at all? Even a few inches will give you a better look overall. The scale for the tiles will also affect how it looks between the standard backsplash height and the rest of the wall.

No, dont do it. End it at the end of the upper cupboards. Paint the wall then hang art or shelves ot whatever.

I would end back splash at the end of the upper cabinet, and treat the remaining cabinets like a sideboard. Since your house is small, hang an arrangement of mirrors (that work with your back splash) to define the spaces and to reflect light.

^^^^^ yes, yes, yes

You have plenty of white on white on white. Keep the backsplash in the kitchen. I would separate the kitchen and dining area cabinetry if it isn't too late.
Add your color backsplash in the kitchen and repeat some of that color in art for the dining area. A rug for the dining area would add additional color.
A rug will also define the living room area in your open concept space. I would buy a rug large enough to hold all the living room seating pieces and occasional tables. Do have some taller cabinetry or an entertainment armoire to vary the sight lines.

I think it depends on the backsplash to be honest. Since you have so much white, if you were doing a darker backsplash, say navy or gray, I think it could be a really cool, almost "statement wall" kind of thing. But if your backsplash is white or a light color, it will look like a diner or public bathroom.

I too wonder if you can remove that run of cabinets into the dining area. Or at least separate them by removing that first set of cabinets just past kitchen and use a completely different counter for remainder in dining area - like butcher block.

I have a small house and small open living/dining/kitchen too so get the wanting to be cohesive but noted that a similar model to mine across way did something similar to you and honestly instead of making it look cohesive it just makes it look like one big kitchen. That look in yours will be similar once you add counters and pulls or knobs.

I think if you can you would be better to remove them and get a nice complimentary sideboard if you need the extra storage. Add cohesiveness with furnishings and artwork instead.

I agree about having a break between that run of lower cabinets and the rest of your cabinets. i think it would define your dining area better. It looks odd to me to have that long expanse of cabinets.

You do want your dining area to be different so if need be, try hanging a large piece of art above the rest of the cabinets.