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Having some amount of caution for a novel vaccine for a novel disease with novel vaccination types seems reasonable. These vaccines are the first mass vaccinations with mRNA or the first mass vaccination with modified adenovirus, depending on which one you get. Personally, the risk from the disease outweighed the risk from the vaccination, but I also wasn't anywhere near the front of the line to get one.

Also, my child participated in a "long term" study on a childhood vaccine reformulation, and long term just means one year. So, if there were side effects outside of that period, it wouldn't be found from long term studies, it would have to come from some other research. Of course, small effects that show up years later is going to take a long time to pin down, and would have required a very large study group to notice statistically.

Realistically, if there is some negative side effect that takes years to develop and only affects a very small fraction of people, we won't know that it's related to any particular vaccine for a long time. And we'll figure it out from epidemiology studies, not from safety studies.