But note that you can not sell your organs, because that will (and does on the black market) quickly create highly coercive contracts between individuals, or worse organ robbery. You can, however, donate your organs.
I would see a similar scheme for your digital data. That, most of it cannot be sold [1]. It can be donated by your positive assent, but the receiver (businesses and such) are highly regulated to ensure they don't exploit you or society using that data.
[1] I concede that there might be certain types of data that could be sold, though I cannot think of an example.
I find it greatly detached from the reality of what is known about the historical personalities that framed the constitution to imagine anything other than them being absolutely horrified.
Privacy has been an assumed right for a LONG time. And if you, right now, went up to someone on the street and offered them $20 to learn their GPS whereabouts for a day, to learn what their voice sounds like and record it, to learn what their face looks like and be able to search it in photos, to learn when they are menstruating, what kind of condoms they like to buy, who all their friends are, who they hook up with, and where they live, hiw many kids they have and where they go to school, I assert that you would find the vast majority of the population would be deeply offended you even had the audacity to ask such a thing, and a few might even call the police.
Privacy is deeply ingrained in our basic social interactions and assumed by most. I think most people just don't have a clue how much it's being invaded because the collectors of such information are careful to hide it behind free gifts, and bury the truth in long, overly broad, complex, highly veiled and obscured EULA's. Then they are more careful still to try and never quite reach the level of using that information in a way that creeps people out by carefully hiding relevant advertisements in enough noise so you won't notice, trading and selling all that information in secret, all while carefully trying to systematically normalize ever more collection and otherwise creepy uses of that data.
Eh, I don't think that's a reasonable take. They're much more rooted in property rights. I guess you could argue they're just restatements of each other. Privacy applies to your person, while property rights apply to your stuff.
But notice the 3rd amendment specifically says "owner", not resident or something similar. For example, if a apartment building owner wanted to allow a soldier to live in your apartment, you couldn't stop them. Obviously any sane lease wouldn't allow that but my point is you couldn't make a constitutional argument against the government saying it's a violation of your rights.
Also, SCOTUS didn't extend the 4th amendment to imply privacy until 1967. Before then it only applied to property. https://en.wikipedia.org/wiki/Katz_v._United_States
(needless to say, I completely approve of the idea of government controls on what other companies can do with my data without my consent)
On the other hand, the main value of your meta data and social media content comes not on it's own, but as part of the larger database. Each individual person could be locally happy with the sale of data (as are sellers of organs on the black market), but globally, you quickly land in a very suboptimal nash equilibrium, which is plagued by coercive relations.
[1] Though recent trends in the reality tv market or adult streaming market are worrying.