I think there's a misunderstanding here about what parts of the study process got fast forwarded, leading to speculation that "long term effects" did not get tested in the way they would normally during vaccine development.

Vaccinations do not get long term effect testing like drugs do because your immune system typically finishes responding within 5 weeks of inoculation. The reason the covid vaccines were approved so quickly is because there was political will to fast forward the funding bureaucracy, none of the clinical investigation takes a long time here.