Nicely researched. Always better to pull numbers from the answer rather than the question, I find!
So basically the maximum amount of people to have died within the EU due to complications arising from the covid vaccine is less than 12k. Obviously, that's still a lot of people but a vaccine is just a form of medicine, and pretty much all medicines can lead to adverse reactions in people.
According to this
https://ourworldindata.org/grapher/cumulative-covid-vaccinations?country=~OWID_EURby the same date there had been 1.39bn vaccine doses administered in Europe. Granted, one is quoting EU numbers and the other is just stating Europe so it's probably not quite comparing apples with apples, but broadly speaking we're in the same ballpark. Which means that statistically you have around a 0.00086% chance of dying by being vaccinated.
Which is only 0.00085% more likely than being hit by lightning in Britain! (according to numbers quoted by the BMJ on the frequency of people getting hit by lightning)