looks like you like a simple mono look... how about a timeless white subway tile?

A plain white tile might work best since you've got a lot going on with the wood tones, flooring, and countertops already. You could look at doing a white scallop design or herringbone design if you wanted a bit of movement and interest in the backsplash.

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I would think about a whisper-soft light green, maybe in a glass tile. I think that would look wonderful with your wood tones (both of them) and act as a bridge with the wood, the counter, and the flooring -- would tie it all together and bring in a gentle element of color.

Fireclay has some gorgeous light greens. Tile Colors | Fireclay Tile

BTW -- I love the color of your kitchen cabs, I'm getting a peaceful vibe.

It looks so nice as is I'm tempted to say just go with plaster -- but finding someone who would give you a durable plaster that is NOT venetian plaster might be a wild goose chase. But it does exist

https://luxesource.com/gallery/contemporary-cream-kitchen-with-plaster-backsplash/

I think a really lightly variegated tile would look nice in your kitchen. I think a basic white might be too stark.

https://portolapaints.com/collections/roman-clay/products/spotlight-roman-clay

Continue the countertop up the wall. Love the cabinet color.

Tell me more about your cabinets. They do not look at all gray to me.

I would do a white tile that matches the counter.

due to the smaller sized space I would get a nice quality white subway... there are different sizes of tiles to tweak it a bit ....basic white tho' for your pretty space. there's actually a bit going on w floor veining/ counter veining/ black hardware/ wood stain on a good number of cabinets. It can be too much if you veer off.