Look at JC Penney online for washable nonslip rugs. You could ask a professional floor cleaning company if there's anything they can do, for example, applying a non-slip floor wax that would protect the finish and make it easier to clean. Or call a floor refinisher.

The house is a rental but we’ll be in it for another 3-4 years. I can’t redo the floors. By awful I mean I’ve never seen floors like these. They feel like plastic wood is the best I can describe. They are warped and there’s areas where the floor is sunken so I was hoping to put a slightly thicker rug to add some comfort but I’m not sure on what pattern/design/color rug to put down. I was measuring so that there will be about 1 ft between the rug & the counter. Any suggestions on rug colors or designs?

Something multi coloured that incorporates a bit of the green should work well. I would then suggest repeating another colour that you pull from the red in other decor such as kettle, linens and some items in the glass front cabinet. Im including the rug below as an example of what I think would work. I think a Scandinavian style would be a style for you to explore.
https://www.houzz.com/products/momeni-novogratz-bungalow-bun-1-area-rug-multi-36-x-56-rectangle-prvw-vr~132372870

Since it's a rental, I'd be hesitant to use a rug whose backing might discolor the flooring, so ignore the JC Penney rugs.

I agree with apple_pie 100%, it happened to me many years ago and I lost my security. Watch out for any rubber backed rug, or even your scatter rugs you have down now, if they get wet the rubber backing can stick to the floor and you'll have to scrape it up, it's a tough call having rugs in the kitchen.

Maybe look HERE