I read “in such manner...” as the actual methodology rather than questions asked beyond enumeration of live people.
Do they use mail, door to door, smoke signals, make everyone go to the home of their birth, town meetings etc.
If that were the case, it would seem to me that Founders such as Madison would have objected to the first Census on those grounds. Instead, he championed questions that went beyond a simple count.
IMHO a certain amount of demographics is necessary and proper - of course, we are saddled with a Congress that habitually goes beyond necessary and proper and instead passes laws that tend to benefit themselves and their sponsors - so I can more that identify with your position!