The Economist has this report on a very large sample data investigation into all forms of mortality for people who have been jabbed against COVID-19 compared to those who have not. This is unlikely to be a direct effect of the vaccine, it is much more likely to be a consequence of sorting:
"Large observational studies can give unparalleled insights into the safety and efficacy of vaccines across diverse populations. However, real-world data is never perfectly controlled. It seems all but certain that some still-invisible difference between people who get the vaccine and those who do not, rather than some unknown benefit of the jab, is to thank (or blame) for the vaccine’s correlative effects. Jabs are not immunisations against mortality."