You seriously underestimate the resilience of people. If there's a global thermonuclear war (or equivalently intentional disaster, like the release of a weaponized pathogen), yes, that could be the state of affairs in a few hundred years; if there's a totalitarian luddite hyperreligious takeover worldwide, also possibly yes; but otherwise, the number of people likely to die from climate change, resource overexploitation, local military conflicts, and so on, is unlikely to top a couple billion. It would still be the worst calamity to befall humanity in written history, but we're not getting to the hundreds of millions involuntarily. We might decrease our population that much "on purpose" (either literally on purpose, or as we are doing now in industrialized countries with enough incentives that point in directions other than having children that the birth rate drops), but the carrying capacity of a +10C Earth with no fossil fuels and depleted mineral resources and a roughly-modern-wealthy-nation-equivalent standard of living is still in the multiple billions.