Serious question: but when is there ever data on long-term effects for a vaccine?
The flu vaccine changes every year.
I was in the age range which had the initial mass vaccination for polio. No data on long-range effects, but we knew the effects of polio and our parents were eager to get us vaccinated. Even today, it would be very hard to determine the effectts of that vaccine long-term, simply because almost everyone got it and just so many confounding factors over a life-time.
Yes, it is true that the Covid vaccines have only emergency, rather than full approval. I see it as directly analogous to polio vaccinations -- protection against severe harm. Over 600,000 Americans dead of Covid is an emergency, and with the delta version, it isn't over.