I think we’ve migrated for all sorts of reasons that have little to do with climate. Not least is the basic human urge to explore and find something new.
I think it’s bit of both. The area that the hunter/gathers lived in some 300,000 years ago, starts to get warm they move north and visa versa. (Well for half the planet)
Ever see a drawing of a dinosaur with a fern next to it as tall as it is? That’s because the CO2 level was 5xs what it is now (More CO2, bigger plant), possibly due to increased volcanic activity.
Love Geology (although it’s no where close to my love of cooking!) and it pretty much supports MAJOR climate changes even pre-people. (Changes in earth’s axis, sun’s temperature, number of sun spots, volcanic activity, etc.)
I don’t believe anything man does has anything to do with climate change. Some are just looking at it as a way to cause fear and gain control. (Think Klaus Schwab. He talks about it in one of his great reset speeches.)
Remember “OMG, THE ICE AGE IS COMING!!” when we were kids? This BS started almost 60 years ago!