I can’t speak to the actual eugenics of it or Bill Gates’ personal views, and I’ve read some super fucked up shit about poor post-colonial countries being used as essentially guinea pigs for the medical industry. Idk though, googling I’m finding the same thing as you, just anti-vaxxer shit. But looking beyond that, and focusing on the overall discussion of birth rates in poor countries, it’s absolutely not eugenics. It is ridiculous and anti-science to suggest this.

Birth rates are statistically linked to a population’s wealth and subsequently, quality of healthcare. Poverty makes it necessary to have a child for many reasons. A high child mortality rate means a higher likelihood of growing old without children, so it makes sense to resort to “throwing semen at the wall and seeing what sticks,” having tons of babies. This is how it was even in relatively rich western countries before modern medicine changed child mortality from something almost to be expected, to something rare. Plus, in a peasant society, your children would become your workers and caretakers as you grew older. A large family had a much better chance of surviving through harsh times. Healthcare has generally gotten better in the world, and birth rates have plummeted in virtually every single country. Just look at Cuba, after the revolution stabilized and healthcare improved immensely for the general population, birth rates plummeted from ~5 per woman to ~1-2.

Also, access to contraception and birth control is a GOOD THING. The ability to actually choose how many babies you have while still being able to have sex is a huge factor in population growth. Access to abortion is also important, there are far too many accident babies who risk having a shitty life or grow up as orphans. Legal abortion also does not statistically lead to more abortions, it just means safer abortions.

Western countries have very low birth rates because they are wealthy and have much better access to healthcare, while poor countries are plagued by the factors above, leading to much higher population growth rates. So under luxury space communism, with universal access to all kinds of healthcare, with all the most important needs met - population growth would plateau immediately, much faster than is currently being predicted.