As of right now, more than 150 million vaccination shots have been given worldwide, and that is a combination of Pfizer, Moderna, AstraZeneca, and the Russian one, and the Chinese one - and these use diverse technologies, they're not all the same. There has been no rash of deaths associated with any of them. If it were significant, you would be hearing about it, and countries would be suspending their vaccination programs. South Africa has suspended distribution of the AstraZeneca vaccine ... but only because there is concern that the current version of that vaccine may not be sufficiently effective against the particular variant of covid19 that is spreading in that country.
Keep in mind that it is inevitable that there will be people dying a week after getting vaccinated - it is practically a statistical certainty when dealing with such large numbers. The life expectancy of an average human in the developed world, measured in weeks, is about 4000 weeks ... and thus far, vaccinations have been aimed towards older folks who are at greater risk ... and also have fewer weeks remaining. Just because you search the internet and find a case where someone died a week after being vaccinated, doesn't mean the vaccine had anything to do with it! They may have dropped dead of a heart attack anyhow.
To me, a peanut represents a greater risk to my life than this vaccine does.