I read that birth rates are declining all over the place. Animals do this: they slow reproduction when resources get scarce. We're animals, so we do it in response to the widespread perception of scarcity. Because we're human we don't have to wait until we are dying en masse. We can see it coming.
Countries that accept climate refugees will continue to grow for a while. After that who knows?
Perhaps we are like people in Medieval Europe who could not envision any societal order besides the church dominated one they had. Something like 30% of the European population perished from bubonic plague. COVID didn't accomplish anything on that scale but global warming could.
With luck maybe dwindling population will spare us that. If not, it won't be pretty.