It probably is not really doing anything, I would think replacing the nocebo of being infected (or supposedly being infected) by SARS-CoV-2 in the past with the placebo of getting vaccinated (more recently, so you get a recency bias boost) makes up most of the "helping". If not that exactly a similar psychological re-targeting effect is probable.
It's still unknown what causes long covid. Lingering virus is one hypothesis that's still plausible. Indeed some people believe it precisely because the vaccines seem to be helping significant numbers of people (but not everyone, they can also make it worse for some people).
A substantial proportion of long covid cases share similarities (particularly demographics) with other syndromes of unknown mechanism, particularly chronic fatigue syndrome.
By what possible mechanism? Does this imply that long COVID is a result of some small amount of lingering virus?
I was under the impression that long COVID was a result of damage caused by the initial infection - not some continuous infection of the actual virus.