Get tile!

Get tile or run the matching counter material all the way to the bottom of the cabinets

I would go with tile, will be much easier to wipe down behind the sink than with an untiled surface.

Tile only. Not tile and the border if you were possibly thinking this.

I would install tile.

A backsplash should have been discussed and decided upon when you were selecting the counter material. You have paid for that short backsplash which you won’t be using if you have a real backsplash from counter to cabinets.
The backsplash can be the same material as the counter or something compatible with the counter. If you choose tile, it should match one of the colors in the counter.

Remove that 4” stone partial backsplash and do a nice backsplash from countertop on u as far as you can afford. A a min up to bottom of upper cabinets.

Btw, that 4” is going to impact full use of the handle on faucet. So it has to go.

A picture of the whole kitchen would help ...to determine what kind of backsplash would look best...knowing how much area needs to be covered ....whether it will be viewed from other rooms....seeing the style and planned colors of the rest of the space will also help.....

Can you skip the quarter boarder and just do tile?

The 4” inch backsplash discussion has always baffled me. Why remove it before adding tile? I have seen it both ways and can’t say one looks so much better than the other. I am wondering if there is a reason for it other than strictly cosmetic? And if it is just cosmetic, then it becomes just an individual preference.

Is your faucet handle hitting that 4 inch border; it looks taller than that.? What is going around the window and what is the ledge?

For my taste, I think the cabinet may be a couple inches too high. In my non expert, not too experienced opinion, if you can't afford the tile right now, ; get rid of the backsplash or get one half the height, and use good quality kitchen paint. And dry the wall if it gets splashed.

The 4" backsplash was used years ago, to cover the gaps between uneven walls and countertops. With today's technology, where electronic templating is done, you can get a much tighter fit. Hence, we were able to eliminate the 4" and go with all one material on the backsplash which tends to be a more desirable overall look.

I can't post pics from my ancient ipad, but I have been seeing plenty of four inch, or taller backsplashes in high end kitchens. DeVol comes to mind right away. Bailey Austin design did a prep kitchen with a beautiful splash like that. Its on her IG, it may be more than four inches https://www.instagram.com/p/Bx_DicmjBze/

Also the little backsplash isn't pattern matched in the pictures posted so it looks off to see random veins coming from nowhere. I'd do all tile backsplash. Hard to tell what to do in the window.

Tile is the consensus. The proposed idea of removing the four inch backsplash depends upon how well the contractor fit your countertop.. Did he use "electronic templating"? Can he assure you no gap will exist? If he says there will be a gap, then the entire countertop would need to be redone. See link for kitchen without 4" backsplash https://tours.stevenjamescollins.com/public/vtour/display/429996

Ritasj, I love your kitchen! What amazing, furniture like cabinets. Nothing cookie cutter, same old, same old about that space! Consensus did not design that kitchen, style and taste were at work there.

Thanks for the nice words...altho this pic was taken 15 years ago and we painted about 5 years ago...I still love it so much...when we built we didn’t use any new cabinets ...we added the “new in kitchen “ pantry...but had to resort to painting it to give it the personality to live up to all the antique cabs...