The research is complete junk. They don't even distinguish between vaccines. How can anything useful be said if the data review doesn't even attempt such obvious elementry control? And the next question is, if they haven't controlled for elephant in the room variable 1, what other confounding variables are going to relegate this to the back of the class for research?
Concern about possible under-reporting or monitoring of side effetcs is one thing. Exrapolating the conclusions they reach on the basis of such weak nominal data, without even attempting to control for obvious variables, is really bad research.
This isn't mutton masquerading as lamb, it's baked soil pretending to be a shepard's pie.