Online searches sure are frustrating. I have seen read and all sorts of relevant studies and articles that are rattling around in my head and can't seem to find any of them online!
On the subject of the amount of room chickens need:
I recall seeing a video quite a while ago of an experiment where they put a few battery type hens in a cage with walls that would slide out and make the cage bigger. The hens soon learned that they could peck at a target to make their cage bigger, and after some time the walls would slowly slide back to usual battery cage size. Researchers were trying to find out how much space was actually too little from a battery hen's point of view. Again, this was a study from the "industry" and I hope here we are never trying to find the bare minimum space they need, but it is an interesting premise: let the chickens decide for themselves how much room they want. California did enact larger sized cages long before the rest of the nation based on these studies.
I think it was mentioned earlier in this thread that after California enacted the ban on battery hens (2018), egg-producers here have had to re-think breeding egglayers. For so long they had bred lines of egg-layers that would be productive in cages and these same lines were not as healthy or as productive cage-free. So new lines are being developed for the cage-free industry. A small step-in the right direction, at least. Maybe we'll eventually get to all pasture raised eggs and won't see battery hen lines bred at all.
For me, my entire backyard is smaller than some people's runs. Following local regs, I did manage to fit in a coop/run that could have housed 4 full sized hens according to the guides set here on BYC. However, even as a chickens newbie 12 years ago, it just seemed wrong to me, too tight, hence the 3 bantams instead.