But how widespread are the negative side effects, do you have data on this ?

There have been a bunch of studies that have come out, with a range of quality in case selection methodology eg. biased sampling, so its still early days. I've seen estimates ranging from 2% - 33% for effects up to 7 months after infection for mild-moderate symptomatic cases. But generally, it seems quite a serious issue.

This is a good review on whats out there: https://www.nature.com/articles/s41591-021-01283-z