Social science is far from exact enough to predict either eventuality with any confidence.
If waves of tens or hundreds of millions of refugees leaving places they cannot live in any longer begin sweeping across borders, how long will it be before fascist governments, already threatening, and already winning in Turkey, Poland, Russia, Belarus, the Philippines, Brazil, Hungary, Italy, and India take over generally and initiate wars, as they do? Such wars might not go thermonuclear, but they would certainly disrupt fragile global trade networks.
People have had terrible governments before, for most of human history in fact. I do expect global social conditions to deteriorate as climate change strains countries, but that's a far cry from the end of the planet.
As for global thermonuclear war, we could wargame likely scenarios and potential outcomes endlessly until the day it might actually happen. But anybody who tells you with certainty that one will happen in the next 20 years so there's no sense planning for the future (e.g. no sense building a power plant that will be used 20 years from now) is trying to indoctrinate you into a doomsday cult.
Nobody suggested power plants should not be constructed. At issue is what to construct. Starting nukes now brings catastrophe nearer, as they displace exactly zero CO2 output for many years, vs. alternatives that start displacing CO2 output immediately.
If waves of tens or hundreds of millions of refugees leaving places they cannot live in any longer begin sweeping across borders, how long will it be before fascist governments, already threatening, and already winning in Turkey, Poland, Russia, Belarus, the Philippines, Brazil, Hungary, Italy, and India take over generally and initiate wars, as they do? Such wars might not go thermonuclear, but they would certainly disrupt fragile global trade networks.