It isn't necessarily overpopulation that is driving the policies in the US. But the Ponzi scheme we call Social Security and Medicare does require an ever increasing number of working age people. That's why the government is so determined to keep importing large numbers of people.
I remember when "overpopulation" was a major talking point of the left. And some people chose to have smaller families. But now we supposedly have a shortage of workers and need to import people, even though more American adults are not working.
The "geometric growth" the government cares about is the growth in people paying Social Security and Medicare taxes who are years away from receiving payments.
You are right that people watching large-scale changes in the planet are worried about a different kind of growth than those who want to either increase or curtail the number of workers for business reasons.
Those are definitely two different things, but it is the growing planetary scarcity of everything and the decreasing quality of everything, especially visible over the last few decades, that make a lot of people nervous about the future and are the cause of both.
I resisted bringing religion into it until now, but ever since the Garden of Eden disobedience we have been up somebody’s creek, I’m not sure whose.