I use a piece of plywood covered with vinyl tiles. On their levels I put fleece over top so it’s not slippery, but left the bottom level bare. I also have used a hard plastic carpet protector (the kind meant to be used under an office desk/chair).

I thought I replied to this, darn.

I am a fan of a two-layer system, where the bottom layer is the waterproof, indestructible, stable foundation, and the top layer is the comfy, washable layer. I have a sheet of cut cloroplast as the bottom layer, and cut carpet squares on top that I can clean, and if they get gross, I can recycle them and replace them.