At most an antic fatigue mat at the sink other than that I jate rugs in kitchens IMO tripping hazards and one more thing to wash

I use three neutral-colored (close to my floor color) rubber-backed thin rugs from Target in front of the areas where drips and spills happen most often - the sink, stove, and frig. They are thin and firm enough that they are not trip hazards and once a week when I clean the floors I toss them in washer on quick cycle. Under the table and chairs, I have a thick, multi-colored rug to bring softness and color to entire area.

I would not do rugs anywhere

I use a rug only in front of the sink and it's exactly placed evenly under the faucet above so, when you walk in, you don't see a crooked rug. If you really want a full lenth one across that area, it could look fine but I tried one and it kept moving due to the length so I took it up and got one oriental for just the sink. Your floors are so lovely.

A vinyl floor runner across sink (go as long as you can afford) and complement wall color. Anywhere else will be a nuisance and the other end of room already has enough.

If you feel the working area feels empty, a portable island will help and also be functional.

I love my ruggables! They are not tripping hazards at all because they are very thin, but also have a rubber (fatigue) pad under them. They don’t move and you can wash them. I would put a long runner across the whole side.