4100K is really, really white. It can look quite sterile. I have found 3000K to be sufficiently bright enough for kitchens. Do you have any freestanding lamps that you could buy different temperature LED bulbs for? That might be a good way to test out the light quality in the space.

Go with brighter white on ceiling. Will feel Brighter. The same tone on walls n ceiling will throw off the visual.

When the tile is up, but has not been grouted yet, there is the illusion of contrasting grout. It won't necessarily look gray, but the shadows will give an idea of what the contrast will look like. That might help you decide if you like the look. I have white grout and do not find it a problem, but I do have a regular range with a higher back to it, so the area behind my range is partially protected from splatters. You do not have much backsplash behind your range as it is in a pass through area, so I don't think keeping white clean will be too much of an issue. Given the simplicity of your kitchen, I think the contrast would be pretty, but it will look good either way. The tile guy will have a bunch of silver / grays for you to choose from. I personally would do a light silver gray rather than a dark one.

Here's a small lesson I learned...Medium gray cabinets and light gray walls together are boring! I didn't want white kitchen cabinets, so I went gray, and a very light gray paint. It's looking very bland. I'm hoping the vivid granite I chose livens it up when it gets installed! I do have a solid white tile backsplash that I saved from the demolition hammer!