No, they unfortunately aren't compatible.
The Rift CV1 controllers only work with the CV1. The Quest 2 controllers only work with the Quest 2.
The Rift-S and Quest 1 both use the same controllers, so they are compatible with each other, but they are the same price to buy individually.
The Rift-S doesn't work well without controllers, it will complain that it can't find them and most games for it won't work.