You can refinish the hardwood floors that you have to whichever color you desire. No reason to shop for new floors.

The sample closest to the cabinet looks fine. It complements the built in without matching it. The other sample is too light.

You can sand down hardwood floors, add new ones and then stain all of them the same color.

My current floors are engineered so they can’t be sanded and refinished.

Stop investing in one and done floors. Purchase real wood, it will last you 100 years.

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Agreed - get real hardwood floors this time around. I have had dogs and lived in 170 year house with original floors that held up to more than a century of children.

Engineered hardwood flooring can be sanded and refinished. 6mm as many times as tongue and groove solid in many cases. 3mm at least once. 4mm would not be a problem. You do want to take into account the micro bevels when determining the amount of surface to remove. Especially when going from dark to light or the opposite.

These are videos by refinishing pros-

The oak flooring in the second video is not NAmerican red or white oak. It's English or European oak, a different species without open grain.

Because this flooring project is a substantial financial investment and it'll affect your homes value, I'd consider not trying to match the finish of the cabinet. I'd refinish the cabinet a lighter less yellow tone. This will allow you to choose flooring in a paler brown with a clear water poly matte finish.