Multiple countries have already started the COVID-19 vaccination.
Local media covered this extensively and I saw that many medical doctors and researchers arguing that the vaccines are very safe because they have already been tested on dozens of thousands of volunteers before being released.
On the other side, I saw some posts made by what seems to be vaccine experts arguing that there was not enough testing being done and some side effects show up only after many months or even 1-2 years.
This somewhat contradictory information is confusing for the layman: the media message seems biased (it is very safe despite short testing period) vs. some expert's message that seems to make sense (that's why all the other vaccines require so much testing time before they are released).
My assumption is that the vaccine benefit (prevented deaths and ICU cases + economical problems) greatly outweigh the worst long term side-effects as clearly put in this article (emphasis mine):
Granting emergency authorization is not the same thing as the vaccine being officially licensed and approved by the FDA. It means that, given the life-threatening emergency of the COVID-19 pandemic, public health, virology, and infectious disease experts agree that the benefits of the vaccine outweigh potential risks and side effects. However, Pfizer has said that it will seek full approval by April 2021.
I am wondering about getting more details about the emphasized part. I am aware that nobody can know for sure what the vaccine's long-term side effects, but I expect that experts might have an educated guess based on the vaccine type, pathogen type, etc.
Question: Are there any educated guesses related to the type and probability of severe side effects caused by the COVID-19 vaccines?
By severe and estimations I expect something along the line of: "there might a 1:50K chance for a vaccinated person to develop an auto-immune disease".