All vaccines were tested through a usual 3-Phase protocol – starting with a small group to select the dose, 2nd group to verify safety and 3rd to verify both safety and effect. The only difference that everything in the process was compressed in time – every step of testing (and production) was done as early as possible, and many people were involved in trying to achieve this success.
Some might be confused by the fact that, of course, testing was limited in time. Many _medicines_ are routinely tested for years to ensure safety. Note the difference between medicines and vaccines. If you look at statistics of recalls over decades, there are medicines that are discovered 5-10 years later to have undesirable side effects. I did not see vaccines having a similar effect. The difference is
that medicines might be taken over years, while vaccines are finite events, so potential side effects are found out quickly.
All of that is, of course, water under the bridge. By now, all of the vaccines were tested over several years and billions of people. Some possible complications,, like myocarditis, were analyzed and found to have some elevated risk but lower than risk of getting sick by the virus even for the healthiest categories. A couple of vaccines were not recommended for some sub-populations. By now, everyone had a multiple combinations of vaccines and infections (hopefully, in that order) and effect of additional ones is way lower than the first events.