You're picking the wrong direction. When you pick from things with the least selection (appliances) to the most (paint colors), your choices are always expanding.

You are right. However, I felt in love with the tile. Sigh!

I would simply choose a solid color. You want the tile to be the star, right? Notice how in your inspiration photo there is only the tile and a solid color: charcoal. In your case, you're adding a "medium to dark walnut". So, now you're saying you want to add another.....pattern? With more colors?

if it were me: I'd do a charcoal colored cabinet with a matching solid charcoal colored countertop (you can match cabinet paint to the solid charcoal countertop you choose: quartz or corian). Only then will you get anything like the effect you see in that pretty photo.

No, I don’t want to add more pattern. On the contrary. I’m trying to find a compatible simple surface that will not clash with the tile background color and I’m having trouble with finding one. They are either too whitish or too grey.

I like the idea of the walnut cabinet, still. It picks the brownish of the tile and it is a continuation of the furniture in other rooms. I wonder if a totally white marble would clash with the warm/yellow overtone of the tile. The sink, bathtub and commode will be white, too. What do you think?

Pick a plain white quartz that matches the white background in the tile. Find a local counter fabricator that carries a large selection of quartz brands so you can find the right white or go to several shops so you can find the right white quartz.