I don't think this would do a lot to decrease the population, even if the vax was killing mass numbers (which it isn't). For example, if the vax wiped out 80 million people on its own, the human population would still be 99% as large as it was before.
I do think they both lied and exaggerated about the safety profile of the vaccine. They were overconfident about their initial findings, which dismissed some early concerns (such as the irregular menstruation), and they also likely simply covered up various potential safety issues. There is a reason why other vaccines go through years of trials before being released to the public. It's not just because of lack of resources or funding -- it's because time is an important factor when it comes to observation of vaccine side effects.
I never believed this "almost completely safe" bullshit about the vaccine. I had arguments with various people about this back in 2021, including some in the medical profession who talked down to me. I did -- and still do -- believe that the vaccine was substantially less risky for me than getting original COVID or Delta at my age. But was it a risk? Of course.