It is still very early in vaccine trials. There are anecdotal reports of an increase in non-Covid health problems (e.g. reactivation of dormant infections that had previously been suppressed by the immune system) in those who had already recovered from Covid, then got vaccinated. That's separate from the tens of thousands of reports in VAERS and non-public (HMO) adverse event reporting systems for all Covid-vaccinated people, whether or not they were previously recovered.
VAERS suffers from some serious data quality problems. It isn't a representative random sample. No one really validates reports to determine if adverse events were actually caused by vaccination. I suspect that some anti-vaxxers just straight up submit false reports to push their political viewpoint. At most VAERS provides some clues about where to focus real research.
Yes, hence the reference to private HMO databases. CDC VSD (Vaccine Safety Datalink) is not public, sometimes we get data snapshots when CDC is investigating specific adverse events, like blood clots, https://news.ycombinator.com/item?id=27464528. There are people with access to both VAERS and VSD for trend signals, including doctors with private data from seeing patients.
