there is data out there and there is actually a vaccination injury register with over 110k incidents reported in Australia alone.
There is, as there is for all medicines in the vast majority of countries; it is nothing to neccasrily get excited about and is standard pharmacovigilance.
"Pharmacovigilance is the detection and assessment of adverse events related to any drug used in clinical practice. In Australia adverse events can be reported to the Therapeutic Goods Administration. Reports are encouraged, even if the drug is old or the prescriber is only suspicious of an adverse event."
There might be "110k incidents" but this figure alone does not mean much on its own.