Forget a backsplash. Work on a lighting plan first. You have insufficient lighting to be able to pull off such a dark color. You need a lot more recessed lights.

I wouldn't "forget" a backsplash. Nor would I assume that you haven't thought about lighting.

I would, however, make the backsplash decision after the cabinets and countertop are in place in your kitchen. That's the only way you'll get an accurate reading on color, undertones, etc. If you search dilemma threads along the line of "I hate my backsplash," you'll find that most buyer's remorse comes from picking out the backsplash tile prematurely, in a showroom, using small samples of the countertop, flooring, and cabinet wood. You'll have a much better outcome seeing the interplay of colors, undertones, patterns, reflective properties, texture, etc., and how they'll work with your other finishes in their final installation space.. You'll be much, much happier. Good luck!

Sophie is right - you cannot possibly decide on paint or a backsplash until your lighting is updated and installed. Your cabinets are VERY dark, as is the wall paint, and your window looks out onto a porch, that blocking a lot of the light. Light is everything in a kitchen - start working on yours before you make any further decisions.