In summary historical population projections have been pretty accurate but not in the way you expect.
*One thought is that because current date may become a historical inflection point similar to the first half of the 20th century, current date demographic statistics may be too important to put much stock in. Sobering.
It's what I expected, what the UN predicts follows the agenda of the day. Previous it was the fear of some enemy population and now they are trying to normalise the idea of population reduction.
Unfortunately pre-1950 demographic prediction is a little harder to find. I wonder why*
Anyway a reliable source is found here: https://ourworldindata.org/population-projections
In summary historical population projections have been pretty accurate but not in the way you expect.
*One thought is that because current date may become a historical inflection point similar to the first half of the 20th century, current date demographic statistics may be too important to put much stock in. Sobering.