We are within 500 years of creating millions of self sustaining spaceports. We are within 500 years of AGI. We are within 500 years of understanding quantum gravity. We are within 500 years of fixing biological death. The order we get to those and how they interplay and change the world matters so much that it doesn't make sense to worry about making predictions.
But there is no reason to expect better. All the signs point there. Global climate disruption destroys crop yields in tropical and subtropical places, creating political instability. Millions, then tens of millions, then hundreds of millions of refugees flee toward higher latitudes. Nations at higher latitudes elect fascists to repel them. Fascists start wars, wars disrupt trade, economies collapse, nuclear weapons come out, boom.
It would be nice to be wrong about this, but it has all started already. 70M+ Americans voted for fascism. Brazil, Turkey, Hungary, India already got it. Germany, France, UK, Italy, Poland threaten. China and Russia fell long ago. Europe is already strained by the first few million refugees.
Sending the hundreds of millions of refugees on to Siberia and the Yukon could work, in principle.
Climate instability would unlock changes that one by one cause feedback to worsen the situation irreversibly. The bio diversity that prevents this, we actively destroy every day.
You state these "we are within 500 years" as if they are certainties, but you show no evidence for any of them. The only one I consider even slightly likely is that we are within 500 years of understanding quantum gravity.
So... evidence? Argument? Just stating baldly that it is so is not very convincing.
I've seen that article. I don't find it convincing. Start with the first screen: An exponential graph does not have a sharp kink in it just past where you are standing. The rest of the point is valid (an exponential curve means that the next bit if change will be faster than the last bit, and that's going to surprise you), but he's cheating to try to make the point more visually dramatic. It implies "there's a discontinuous first derivative coming almost immediately", when the argument is actually that there's a continuous increase in the first derivative.
So, yeah. Overselling the case, in the graph on the first screen.