"assuming no other limiting factors" is doing a lot of the heavy lifting there.

Seems that greenhouse experiments would allow us to get a pretty good estimate for the effect of CO2 on yields, so actually I wouldn't think we'd need to do that much assuming?

I think what they're getting at is the most common limiting factor for plant growth is almost never CO2. It's usually Nitrogen, or another two of the macro (P,K) or micronutrients.

Actually, they say, first page

"Increasing CO2 has driven global greening: over the last 40 years, half of the world’s vegetated area has undergone greening, of which 70% is attributed to elevated CO2 (Zhu et al. 2016)"

Right, but the study is titled "ENVIRONMENTAL DRIVERS OF AGRICULTURAL PRODUCTIVITY GROWTH" and the OP comment included the word "agriculture" right before quoting the study.

Seems this whole thing got rather confused.

That, and weed management, and GPS assisted machinery.

Pretty much every agriculture advancement since the tractor and other machinery has been getting around the limiting factors of plant growth.

Commercial greenhouse growers have been using CO2 supplementation for nearly a century. If CO2 is the limiting factor (which is not always the case), the difference in yield can be phenomenal.

In an industrial greenhouse setting sometimes CO2 is pumped in for yields.

So one of the climate feedback loops we forgot to consider is more CO₂ -> more food -> more people -> more energy consumption -> more CO₂?

"more food -> more people"

That association has broken in the modern era:

https://www.statista.com/statistics/268083/countries-with-th...

These are countries that are not limited by starvation, with plummeting populations.