Thing is, this sort of thing happens all the time. A prominent and current example is cops and fentanyl. If you listen to cops, they will tell you that just being in the rom with fentanyl can be deadly, breathing it in can be deadly. I'm not sure where this started but it's become a problem because cmany people believe it, leading to cops having psychosomatic panic attacks at the prospect of fentanyl exposure [1]. This story has become so effective that many people disbelieve that it's BS or are surprised to learn it.
So the intersting question is: what purpose do these sorts of stories serve?
With fentanyl, it squarely fits into "copaganda", spreading the idea that being a police officer is super dangerous. Not-so-fun fact: it's more dangerous being married to a cop than it is being a cop (eg [2]).
Another example of this is inflating the numbers of line-of-duty police officer deaths with Covid deaths, particularly because it includes officers who refused to get vaccinated [3].
Fear of crime serves a political purpose. Crime is lower on pretty much every metric than it was 20-30 years ago where the last big panic set in the mandatory minimum mania and the carceral state exploded.
So the obvious conclusion to draw from what purpose Havana Syndrome serves is either selling the story of how bad and dangerous Cuba is and/or how dangerous it is to be a foreign official (which is really a proxy for CIA).
[1]: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7492952/
[2]: https://www.theatlantic.com/national/archive/2014/09/police-...
[3]: https://www.theguardian.com/us-news/2023/mar/03/covid-police...