People have difficulty separating evaluation of the problem (the science)...
I think wieghing and counting are methods pretty fundamental to science. Hence my suggestion.
Price can make a good proxy for the amount of materials used and energy burned to make the thing. Outside of things like the fashion industry where brand names command high prices for nothing much.
All in all a good start to any scientific investigation of this issue.
It seems to me that after that one should not be looking at the Pi in particular. It's just electronics like all the other electronic junk we have around. Much the same components and materials are used, much the same manufacturing processes.
Those capacitors on the board for example. What are they made of? Where does that come from? What damage to the environment is done by all that material extraction and manufacturing processes. I read that tantalum capacitors are problematic.
The capacitor problem is common to all the electronics you have, in you Pi, in your PC/laptop, in your phone, your TV, your car, your light bulbs....
Then what about the resistors? What about the actual silicon chips, the packaging, the board material the connectors, the plating on the connectors....
Chasing down the supply chain of any one of those items to the end would no doubt produce interesting results.
Memory in C++ is a leaky abstraction .