Even if carpeting isn’t the right stuff, I’ll need to put something under the cat feeding bowls — to delineate the area (otherwise they and I push or kick the bowls around) and to keep spills from the floor. Maybe a piece of lightweight plexiglass?

How about something like this for the cat bowls: https://a.co/d/9abLBdZ It comes in numerous sizes and colors; is absorbent; and is easy to clean. I have one and like it very much.