The tiled backsplash usually sits just off the countertop by an 1/8th inch or so and the gap is caulked. The caulk can be cut away and the countertop should be able to be removed without damaging the backsplash. That's in a perfect world. Some installers set the bottom course of tile right on the countertop. Less clearance. Depending on how the countertop is attached to the cabinets below, that can affect things. The shape of the counter. A straight run or and "L" shaped? Are the ends open or captured? How the countertop is constructed? A slab of stone? Or a tiled-in mud bed? Sometimes the countertop needs to be sectioned out in pieces. In general, the backsplash can usually be preserved, but getting the countertop out might be ugly, especially if it's piece by piece. So..."it depends".

I think butcherblock would look nice on the counters. A white backsplash might be too much white. You might consider a pastel-colored tile in one of the soft blues or greens from the rest of the house. (This may mean you need to change wall color to go with the tile, are you OK with that?) Have you considered updating the knobs on the cabinets?

I agree with the suggestion to keep things light. However, as someone who loves color (including the blue you're considering), keep in mind that if you can modify your lighting, you should do that first and then decide whether you still want a darker backsplash. Any color or shade will look different under different lighting. If at all possible, install undercabinet lights and maybe cans spaced around the perimeter to replace the existing ceiling fixture. Then it will be easier to tell whether the improved lighting can keep the space from becoming too dark if you do a blue backsplash tile.

I think what you are considering would be lovely. Don’t get hung up on design terms to the point that they limit your choices. I assume that, when you install new counters, you will eliminate the 4 inch backsplash.