From the FDA web page located at https://www.fda.gov/patients/drug-development-process/step-3-clinical-research

"Phase 3 studies provide most of the safety data. In previous studies, it is possible that less common side effects might have gone undetected. Because these studies are larger and longer in duration, the results are more likely to show long-term or rare side effects "

So, there you have it. "Phase 3 studies provide most of the safety data." And it is the Phase 3 trials that all of these vaccine studies are cutting short.