https://www.nature.com/articles/d41586-022-01453-0

tldr, not that effective as expected but studying long covid is problematic cause it's hard to diagnose due to many diverse symptoms overlapping with other illnesses...
still, if you don't get one due to vaccine then you can't get a long one obviously. also if you get a very mild or unsymptomatic due to vaccine then you also can't get a long one...