Thank you for your excellent posts summarizing multiple sources of information across domains of energy and material limits of human development, ecological economics etc. I am still reading through your in depth 3-parts works as I speak, and I am finding many useful sources of information for my further reading.
I happen to chance upon this discussion while browsing around, and decided to create an account to reply to this discussion because it is a topic of great interest to me.
I think the main reaon why you believe that Corentin's argument on EROI affecting percent of GDP required to maintain energy production is a conceptual mistake, is because you have assumed that cost of production (of energy producing equipment) is not linked to energy use.
However, the basis of the EROI argument stems from biophysical economics, and is based on the key assumption that the vast majority of economic activity and economic value are in fact embodiement of energy. One may or may not choose to agree with this assumption, but if you do take this assumption to be true, then Corentin's point that for e.g. a 2:1 EROI needs roughly half of society's resources is correct.
So in the simple equation that you described:
Because we assume that economic cost of production of anything is directly related to energy, then , where is some factor describing the economic cost in terms of energy.
Substituting it in the energy cost equation, we get
is exactly the definition of EROI of the energy producing equipment, and thus .
Furthermore, with the same key assumption, the total economic output, in other words GDP can be also be expressed in terms of total energy produced or demanded by the economy, i.e. .
We finally obtain that:
If the scaling factor and between economic cost and energy is roughly similar for the particular case of energy producing equipment, and for the general case across the whole economy, then EROI approximately determines the proportion of the cost of operating and maintaining the energy system against GDP.
The key assumption put forward by the biophysical economists has been argued both through first principles and empirically (well explored in this textbook of energy and biophysical economics).
Hall, C. A., & Klitgaard, K. A. (2011). Energy and the Wealth of Nations. New York: Springer.
You probably might have came across it already, but the Good Food Institute (GFI) has compiled a research funding database for alternative proteins (here).
Overall I think having collaborators that have the expertise and facilities to perform biological experiments and bioprocessing may be quite crucial. My experience is that at this moment, publicly available data are scarce and insufficient to support purely computational work in this field, unlike say cancer research where loads of multi-omics data are available for data mining and modeling.