Conceptually, this is very close to the existing functionality of misc-move-const-arg, which is why I'm adding it here and not creating a new check. For example, for a type A that is both movable and copyable, this
const A a1; A a2(std::move(a1));
is not only a case where a const argument is being passed to std::move(), but the result of std::move() is also being passed as a const reference (due to overload resolution).
The new check typically triggers (exclusively) in cases where people think they're dealing with a movable type, but in fact the type is not movable.