Prefecture

The vaccines prevent long-haul Covid because they prevent infection. Confirmed for two, probably true of all of them. In cases where a vaccine does not prevent infection, in most people only the respiratory epithelial cells are infected and the virus does not infect any other body tissues before the immune system fights it off. This is why some people (rare cases) can still spread Covid while experiencing no symptoms even after vaccination.

Your worries are almost certainly unfounded and will reduce vaccine uptake, too. Good work. Keep on.

(Caveat: No vaccine is 100% effective and never will be. Life is a risk. Such it is and ever shall be until we are all in the ground, which is also certain.)