Are there any meta studies that look at cost-per-paper of funded projects?
I think any figures will be moot. Let's take a Nature paper that is signed by people from US, Chile, Sweden, France, Israel, India, and Japan. Whose's funding would it correspond to? All of them? That is a lot of people, so a lot of money, we'll get a terrible ratio. Only the main author? In big collaborations is difficult to pinpoint who that would be. It is easy for a particular manuscript, but not a good representation of the whole.

Let's assume you can trace it down to a specific group. Typically, they have multiple sources of funding, which one should get the cake? Say I publish the paper "On self frying potatoes", whose experiments were funded by the grant "Development of self frying potatoes", it seems obvious. But I could only do it because I attended a workshop on "Tuber theory" paid by my other grant "Theoretical agriculture". We could make the counting at a research group level. How much money they get, how many publications get out, regardless of the source and purpose. That would still have the problem of how to count collaboration papers.