Do we have e.g. estimates about what happens to food production? Or is the problem just so complex that even predicting the consequences is near impossible?
The problem is distribution. Much of the newly-habitable growing zone is currently uninhabited - it's areas like the Canadian Shield, the Sahara, parts of Siberia. Meanwhile, some currently fertile areas like Northern Europe may become uninhabitable, as will densely-populated regions on the edge of habitability like the Middle East and South Asia.
Basically: expect wars and death, then abundance for the survivors.
https://projects.propublica.org/climate-migration/
Two things to note from the infographics.
In the first map, the US habitable range moves north, then west. Look at what happens to South America. (Sadly, it isn't a world map).
The second to last map talks about crop yields directly. Look at the scale. They're predicting a 20% increase in yields in places like Wyoming and Montana (which are not exactly bread-basket states), and 50-92% losses in yields for California's central valley, and most of the US South. Yields in other countries might make up for it (I doubt it), but the US's agricultural yields are set to collapse.
But its shape is dramatically different. Key areas include the Dakotas, Montana, parts of the Basin & Range provinces, Modoc County in California - basically areas where virtually nobody lives now. Meanwhile densely populated parts of the American South, Texas, Florida, and the Southwest literally are becoming uninhabitable through wet bulb temperatures and sea level rise.
The crop yield picture is complex too. It's not actually true that we're looking at 50-92% losses in California's central valley. We're looking at ~13-44% in the southern Central Valley, as well as the Imperial Valley (basically those areas irrigated with Colorado River water). Also looking at 6.5-15.8% increases in other regions of California like the Salinas Valley, Bay Area, far north coast, Modoc County. Central Oregon and Washington and the Great Lakes region stand to benefit as well - these are not areas with large current agricultural production.
Expect upheaval. Humans don't do well when some people benefit and other people die for completely random reasons.
Since then, people say that the above is weak evidence, and are generally in denial of the science. As of a year or to ago, we've been able to measure the slowing and coming stoppage of the Atlantic currents. There's over 50-50 odds that some people reading this will live to see the next Eurpoean ice age. Much of France, Germany and things farther north are likely to end up under a glacier.
AMOC/gulfstream shutdown is not a given, there is still scientific debate about it. But the scientific evidence is starting to pile up, along with evidence that circulation patterns are weakening right now. If you Google [amoc shutdown] you can read a quick overview.
This ignores unpredictable extreme weather destroying entire harvests.