I want to address a very legitimate question that Aldebaran raised re counting. As you may know, there was a time when everyone (in the UK, I believe) who died - even if hit by a truck - within 28 days of getting a positive covid test was considered a covid death. Even though this seems suspicious, and even though the anti-vaxxers have leapt all over this, there is, I believe, a solid explanation as to why this is indeed a "fair" way to count covid deaths. I have provide such an explanation in this thread. Fine.
The question that Aldebaran raised was "why is it not appropriate, then, to count everyone who has died within 28 days of a vaccine as a vaccine-caused death?". Fair question.
Let's look at covid first. Let's say that 5% of all people over 60 who test positive for covid will die because of covid. Let's say that 80% of those who die due to covid will die within 28 days. Let's suppose you get a positive test result on 1 January. Your odds of being dead by the end of January are then 0.80 x 0.05 = 0.04 (4%). What are your odds of dying of something else? Let's say we restrict ourselves to people over 60 and assume that everyone will be dead by 80 in the absence of covid. Doing some simple math, your odds of dying in that same month of January from something other than covid is about 1 in 250 - 0.4% (there are about 250 months in the 20 years from 60 to 80 and you will necessarily die in one of those months).
This is the key takeaway: assuming that you do die in January, it is about 10 times more likely that you will die of covid than of something else - remember, in this scenario, you tested positive on January 1st. This shows why this "count every death within 28 days of a positive covid test" strategy is actually not unreasonable.
What about vaccines now? Same idea - you get vaccinated on 1 January and you are dead by the end of January. Are you ten times as likely to have died of the vaccine as of any other reason?
I suggest the answer is obviously no. And, therefore, it would not be reasonable to count every death within 28 days of a vaccine as vaccine-caused death. In order for your death to have been 10 times as likely to be vaccine-caused as "other-cause" caused, the vaccine would need to kill 4 % of the 60 and over people who take it within a month.
And that is not remotely the case.