What kind of exterior paint has a fine sand paper-like backing, is it a primer?
I believe what you think of as paint is actually a skim coat.
Skim coats used for covering stone and concrete may have the paint or a pigment mixed in.
Your photo is not clear to me and I originally did not open the question because I don’t know of a paint that is like cardboard.
I do know (cement &amp; sand) or other stucco like coatings have been used to cover stone and concrete and make a “new” looking finish.
In some cases when the skim coat is getting weathered folks painted them and
Sears used to have an “elastic” or rubber like coating that worked on “everything” if you were to believe the salesman but this was +30? Years back possibly put on top of a skim coat it might feel that way today I don’t know any one that purchased that product but believe the “sand” base is what is left of a skim coat.