Z, I mean papers in research journals that compare health statistics on people after taking a vaccine with others who did not. A number of of them uncovered elevated risks from the vaccines, like myocarditis in young males. Europeans changed recommended vaccines for younger population based on some of this research. There was also a finding that having more time between two vaccines was safer. Etc. Also, when you put even worst estimates of the vaccine risk v. virus risk, for all groups, risk from virus was higher. Researchers by now have access to millions and millions of health records, and conclusions seem to be pretty definite.
As to sudden deaths, I think those are attributed to the damage from the virus itself. Virus seems to be affecting various organs in the body, leaving lasting damage. this might be especially true in communities that were totally uncareful and people were exposed to multiple versions of the virus (wuhan, delta, omicron).