There are going to be more self-reported cases for adverse effects when there's a huge body of people (i.e. the whole country, eventually) getting vaccinated (twice if Pfizer or Moderna), while there are active scare campaigns about the vaccine, alongside the normal heightened scrutiny and anxiety that people would have over getting a newly-developed vaccine that was produced in a record amount of time.
Yes, I would anticipate a record number of adverse effect reports. If someone got a tummy-ache from their Tdap shot, they probably wouldn't report it. If someone got nausea from the Pfizer vaccine, they're more likely to report it, because it's A- they could easily believe that it signals something potentially dangerous to the person, and B- literally important for further research of the vaccine.
It's almost like the context of this historic event matters.