Like "Long COVID", "post covid vaccine syndrome" is probably psychosomatic.
Evidence?
https://pmc.ncbi.nlm.nih.gov/articles/PMC9825049/
Not to say it isn't real. It is. But just like back pain or headaches there's a good chance it's mostly explained by psychology.
Many things used to be thought of as psychological before we found the underlying physical causes. It’s just as meaningless an explanation as “God did it.”