You might take a look at Carl Shapiro and Hal Varian's 1999 boom Information Rules:
https://books.google.com/books?id=z0hQ12PrERMC&printsec=fron...
As well as their (along with Joseph Farrell) 2004 book The Economics of Information:
https://books.google.com/books?id=-dcLAQAAQBAJ&printsec=fron...
It is perhaps surprising that Varian in particular (Google's Chief Economist) hasn't had more to say about data as a raw material in the years since those books came out.
BTW, your "extracted payments are personal information" formulation may be part of your problem in finding relevant economic theories. At least in part, what is being extracted is actually a capitulation to being locked-in to a system that continuously extracts information. So looking into the economic theories of technology vendor lock-in, as well as the perverse economics of information security may provide some insight.
Back in the '80s and '90s, a topic that I kept seeing was, "where is the productivity?" With companies spending huge money on technology and computerization, there should have been visible gains in productivity numbers, right? But, there weren't. What's up with that?
My thoughts, as a non-economist, when I saw that were of things like just-in-time inventory controls, which were new and entirely dependent on new technology. They needed massive structural changes, which may be why they didn't show up immediately, but still...they were there and the metrics and models of economists weren't capturing their effects until they had completely taken over.
Likewise, the elasticity of labor and capitol sounds very much like the effects of automation on industrial jobs.
"The aforementioned paper by Furman and Orszag argues that what Piketty (and Gabriel Zucman, in their joint work) identify as a high and invariant rate of return on capital in aggregate in fact reflects uncompetitively high rate of return on capital for a few specific, superstar firms in the economy, and the key task is not to manipulate aggregate macro equations, as Piketty (and neoclassical economists more generally) do, but rather to explain why these superstar firms do so much better than everyone else. The short version, according to Furman and Orszag, is rents—payments that some agents, superstar firms in this case, are able to extract from the rest of the economy either because they have successfully blocked any competitive pressure or because they have bought special treatment through the political system, or some combination of the two, in addition to other mechanisms."
Or perhaps we're talking about things like the FAANG set. the extracted payments are personal information---which is not captured in any economic theory I've ever seen---and the moat blocking competitive pressure is the combined result of network effects (bigger databases win) and extensive financial capitalization. (How do you fight a competitor to whom not only is additional capital effectively free but also has huge stocks of monetary capital just lying around in stacks on the floor?)