I have never heard of carpet in a kitchen. Wow! But anyway, what about LVP-luxury vinyl plank? It would be good for the wet.

I would do either Luxury Vinyl Tile or Plank or Marmoleum.

What is your flooring budget in $/sf? It is such an efficient space that you could probably use just about anything without really blowing the bank.

I love porcelain wood look tile laid like wood (not like subway tile with a regular repeated offset and visible grout lines). Tile is tough to stand on for hours on end, but in a beach house you’re not doing that, and it’s fine with water or sand, or whatever the dog brings in. The herringbone pattern below would look great in your kitchen. You may like it so much you decide to rip out the rest of your carpet.

Your tilers will have to tile under the range and fridge, and you might have to adjust the fridge legs a bit to get it back under the cabinets, but it should be no problem, even if you have to adjust the opening a bit.

i'll echo eam44, wood look tile. we have in FR and love it

we used this, Coney Island its the boardwalk series. they have many others, very good quality IMO

I'm not a fan of wood look tile in general, but this is a space where it could make sense. EXCEPT I don't there will be a minimal and weird contrast with your cabinets if you go light, and it won't be the look you are going for if you go dark. What's under the carpet? I think that will affect your all-in cost, won't it?

LVT might be a good option for you. My in laws have a beach house & have dark wood floors. They are white oak with an espresso stain. The water isn't the issue as much as the sand is. That is what is hard on their floors. Yes they get scratched, but it goes with the feel of their home. It's a patina that comes with living at the beach. I'm a fan of light floors, but everyone has different tastes.

Porcelain tile is the ONLY thing that will stand up to beach sand. It grinds all else into ruin.