In any functioning economy there is obviously a correlation.
Bodies have jobs, generate income, and they buy stuff meaning GDP.
Government spends on social services per body, meaning GDP.
Not only are 'warm bodies' a part of economic growth ... 'warm bodies' are the very basis of economic growth in most of the West! If you take out population growth from US economic data, it looks a little more like Europe. If you normalize for lower rates of children ... that explains a huge amount about lagging economic growth in the West.
Populations that require homes, cars, services, food, mortgages - that's what drives the economy.
So to your point - in a dysfunctional scenario, more bodies means problems, but overall no.
How do you think America became the most powerful entity in the Western world and in some ways in the world? And not Sweden?
The story of American economic growth from 1777 onwards includes a lot of things, but if you measure up against Europe, what mostly stands out is body count.
Also - remember that growth is measured in GDP, not 'efficiency' - so as AI does 'more for less' it's technically 'bad' paradoxically, for the economy, as you point out. But as long as we figure out a way (any way!) for the surpluses to be distributed, they will be spent, hence 'growing economy'.
Canada's economic strategy is fully based on body count. The nations banks drive our strategy, and they can't grow any more through competition or innovation - they can only grow through more mortgages, which come from more bodies. So they push for large scale immigration, which is in their self interest.
'AI' is not how the economy will grow.
A sea of new homes, out to the horizon, with a Starbucks on every corner, an IKEA in every neighbourhood, a Toyota in every driveway, and a dozen prescriptions per home ... this is how our current economy 'grows'.
The number of jobs is highway correlated with the number of people (most jobs exist to serve the population). So, population decline won’t help keep (relative) unemployment numbers down.
2008 pop: 304m people. 2018 pop: ~327m people. A 7.5% increase in population across a decade.
2008 GDP: $14.72t ($17.64t inflation adjusted). 2018 GDP: $20.5t. Approximately a 17% real increase in GDP.
The US added an economy close to the size of Germany in just ten years while only adding 23m people (Germany's population is 83m). That's courtesy of increasing output per capita far more than it is population growth.
If every two people in a group have exactly one transaction, then adding 20 people to a group of 100 will create more new transactions than you'll find in a group with just 20 people.
To be fair, when I google for research on correlations between economic growth and population growth, I get a jumble of papers on opposite sides - some pro-natalist and some anti-natalist and some agnostic. (Maybe one camp is considered far more authoritative than the others?)
Maybe it's a nontrivial relationship if it exists, though I'm not convinced anyone knows definitively how the relationship plays out.
2008-2018: total US debt (government, corporate, household, non-profit orgs) increased almost 9% from ca $68.1T to $74.1T, if you trust the numbers (https://www.nwcapitalsolutions.com/project/us-deleveraging-a...)
Every day we read articles about how AI is going to drive massive improvements in productivity, killing millions of jobs in the process. If we really believe this is true, then a shrinking population is what we want, to "soak up" those destroyed jobs. A bonus of massive productivity increases is that real property transactions as a percentage of the economy will shrink too, softening the blow of contraction there.
Real estate is not the first industry to be threatened by changes in the economy! Creative destruction is part of our economic story and there is no inherent reason real estate should be immune from that, or that we should feel special concern about that industry among all others.
In short, I see no reason to believe that a shrinking population necessarily creates a shrinking economy. "Contraction economics" sounds cool but it's just a new name for what happened to the buggy whip industry, the telegraph industry, the canal industry, etc. And yes, maybe the real estate industry too.
EDIT to add: In my opinion a more significant future for economics is accounting for externalities that have typically stayed off the books, like clean water, clean air, a stable climate, etc. Economics has typically modeled economies as open systems, that is, there are "inputs" like raw materials and energy sources, that create economic outputs. But we've conquered the Earth now... with the exception of insolation, the global economy is a closed system. Every ounce of raw material and every joule of energy creates a complementary cost somewhere else in the system. Unless we can account for that, we will fool ourselves about the actual net value we are creating.