The bottom 50% has indeed gotten better (kinda sure but not everywhere) but technological progress is not guaranteeing they'll save everyone _anymore_. Fewer nations care about climate change and taking care of the poorer parts of the world (hope you dont expect me to show why too).
The billion is my number. Almost all scientists and officials underestimate deliberately and naively death tolls. I have a metric that whatever number the new york times publishes for an earthquake on day one, you should multiply it by 100 for the eventual total count. No one estimated a million plus deaths from covid in the US. The moment I read the first comprehensive report from China I assumed 1% of the population will die. Unfortunately in places like India that actually was true. So yeah I do think at the minimum a billion people will die due to climate change in the next 50 years, and billions more will suffer in unthinkable ways. Thats _my_ estimate.
As another comment pointed out, if you care for the bottom 50%, you should be extremely happy about progress over the past 50 (or 100 or 200) years.