We should not forget, that in most countries people who were unvaccinated came under severe social pressure. They often lost their jobs or got banned from social circles. You were basically rendered an outcast by not being vaccinated. So taking the vaccine did not only affect your immune system, but also gave you a higher social status. And there are plenty of studies that show that a lower social status significantly impacts mortality, with lower status linked to higher death rates. This may explain the lower all cause mortality among vaccinated people.