That's a very good question, and the evidence is still emerging, as Dr. Falcone mentioned. Initially, there was some promising evidence to suggest that vaccination does have a protective effect against long COVID, but most recently there was an article that came out in Nature at the end of May suggesting that vaccination was only partially protective against long COVID. The evidence is still emerging, and time will tell as the evidence further emerges.
On June 13th, 2022. See this statement in context.