Humans will wipe out plenty of animals and species on the way to that extinction though (also clearly plenty of other animals are suffering from climate change, see the estimated billion animals that died in Australian wildfires last year, or the baby birds that jumped to their deaths to escape the heat in the PNW heat dome this year, or the bleaching of coral reefs, or all sorts of other ways the climate is killing off animals).

Sure there might be some life that survives the climate crisis after we're gone, but the planet is going to lose most of its biodiversity before then.