well to be frank, cabinets and counters is the bigger deal. What do you have in mind with that? And certainly dont pick cabinets and counters to go with the floor....pick and choose those in accordance to your desire and budget.... whether paint /replacing or a combo ...... The floor tile can be painted / the floor can be replaced. Saying that I like the floor and see a very light green rather than tan walls......They are older cabs/older appliances//kind of undesirable backsplash so the list is not short......are funds available? otherwise wait and get funds and throw down some green mats/a runner to soften the effect of tile for a time ,since you feel its an issue. To handle this space for a renovation approach takes more of a broader look at what is shown and adjacent spaces .The walled in dinette zone, if redone, may be an opportunity to get a different thing going here.... but all openings/walkways/windows etc have to be scrutinized.

What do you like in kitchen looks? You could easily do a cream or white cabinet, or a sage or gray cabinet, or natural wood, all pulling from tones in the floor, so it's more about the color schemes you like. But "accentuate" and "minimize" are opposite suggestions, making me wonder if you actually like this tile enough to work around it?

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So... clearly slate floors can support a range of colors and styles. See what appeals to you!

The floor is closest to the 2nd to last photo you posted. In my opinion, slate with lots of brown/orange tones look best with unfinished or light wood cabinets.

Primarily gray slate seems more versatile as far as decor and paint colors go.

My cabinets have been painted by the previous owner. I realize I said both accentuate AND minimize.
I don’t mind accentuating them if the overall kitchen has a look I like.

I didn’t plan on doing butcher block counters
because I want something more low maintenance.

Photos 1, 4, 8 are kitchen styles/colors I like. I just never see this style with slate that is primarily golds, oranges and browns aka mine.

I think your slate tiles are beautiful! You just need to find the right colors for your walls, trim, and cabinets to get the balance you seek. And some plants. :)

Look into colors that match your favorite shades in the slate.