None of this is going to happen, populations are levelling off and we are getting more efficient, sure there is a theoretical limit but nature will show us that limit and it won't be AI's problem.

Why does AI care if we run out of food? They might restrict our access to energy and critical materials but some people could use a little bit of restraint. Weren't you on a flight to Europe the other day, and downhill skiing? Activities like this will become unaffordable long before life does. If we all lived a basic life and consumed resources within 100km of our home then the earth could support tens of billions, not that that's a rosy picture either.