If you put a wood look LVP next to real wood it is not going to look good. That's why you're having so much trouble choosing one. They don't work. Look at LVT (tile). I actually like your existing floor, except it's awfully dark. So see if you can find a LVT in a color similar to the veining in the counters. Gray/greige will look fine against your wood floors.

I agree. There is a big difference between “real wood” and “a photograph of wood”, that is impossible to ignore when they are side by side.

I also would, personally, spend what it takes for the floor you really want now, and take it out of the appliance budget. Replacing today’s stop-gap floor in the future will be expensive and disruptive. Replacing your current appliances in the future will be as easy as sliding out the old and in the new, assuming standard sizes.

LVT that isn’t faux wood seems like a good solution, if that’s a floor you’d like long-term. If you have your heart set on something else - ceramic tile, hardwood, etc - then I’d get it now.

A good wood flooring company matched the existing wood flooring in our adjacent rooms for our previously tiled kitchen. And the original wood flooring is 120 years old! Now all 3 rooms are close enough that no one knows one of them is brand new!