This could feel right
Layered over a mat
Many people place a yoga rug directly on top of a standard mat. The mat grips the floor, the rug softens the surface. This is especially helpful if your hands and feet get a bit slippery, because the fabric can absorb moisture while the mat holds everything in place.
When I practice this way in a studio, I like the feeling of having “my own” surface, even when I’m using a shared mat underneath. It’s a small way of creating familiarity in a new space.