This seems to be a common misconception. The EUA application is essentially the same as the full approval application in terms of the data required. The normal approval process for vaccines does not require long term following of test subjects prior to approval.
The reason why is that vaccines are dosed once or twice, and for every vaccine weâ(TM)ve ever made, adverse events tend to show up within the first 1-2 months after vaccination.
And this makes sense. Your body is not experiencing chronic exposure to a drug as it would for something like viox. So the main threat is from triggering a faulty immune response that either attacks your own tissue, or enhances disease.
The clinical trials of 10s of thousands of people establish a pretty high safety threshold. Even vaccines with rare problems (J&J) are still very safe.
The 100 million+ that have been vaccinated after the trials completed are also proving the vaccine to not only be very safe, but also highly effective