Hello, congrats on the new car and welcome aboard.

I used to have one from this company on my last car, an XC70 - it was a heavy thick rubber, though unfortunately it looks like they are out of stock:

Travall® CARGOMAT

 

I'm not sure this will help, but Volvo has a trunk mat that is carpet on one side, and molded rubber on the other side with ridges that should help hold your dog's feet. I bought it because the Weather Tech mat that I also have does not protect the back of the rear seats when they are folded. The Volvo mat does because it has two extra flaps. The first flap normally is folded under the main mat and can be unfolded to protect the seat backs when they are down. It is made out of the same material, carpet on one side, and rubber on the other The second flap is a piece of thick cloth that folds out from under the main mat to protect the bumper when loading things. That flap is also visible in the rubber side photo.

In my car I keep the Weather Tech mat on top because I already have it. The part number is 31659555. It wasn't cheap, around $260 if my memory serves me right, but I got 10% off because of a coupon I had. I hope the attached photos help.

 

Thank you both 🤘