I've personally known many people who have had serious medical problems that sure looked clearly like vaccine reactions.
I'm curious how that coincides with no such person reporting their experiences at https://www.lesswrong.com/posts/XnRTP4dq3dkdwwtdS/which-rationalists-faced-significant-side-effects-from-covid. For me this thread was a test about whether I should look more into vaccine site-effects and the lack of reporting suggests that they aren't very common.
Are all those people you are talking about outside of the rationality community? One thing that I would see plausible is that people, who are generally psychologically suggestible and who believe the vaccine is dangerous, have their bodies overreact when they are faced with the more normal vaccine side-effects. Such a dynamic might produce more vaccine side-effects in people you know from a spiritual context than appear in the rationalist community.
One step that could be taken to verify an existing pattern of a lot of vaccine side-effects would be to simply hire a SurveyMonkey audience and see what people report when asked through that channel.
But how in the bajeezus can anyone possibly extrapolate from there to how long it takes to become symptomatic? In need of hospitalization, sure, but how is anyone getting not-heavily-biased data on symptom strength below the hospitalization threshold?
We have people we pay to do contact tracing. There are likely cases where that comes with both asking for symptoms and doing testing.
There was, best as I could tell, active (if unintentional) data destruction quite early on in the pandemic. Maybe it's still going on? Hospitals had financial incentives to find reasons why people who died had died of Covid. Lots of bodies got cremated before autopsies could happen.
From a conversation I had with a doctor, it seems that our medical system generally does a lot fewer autopsies than we did 20 years ago. There seems to be a general culture change here. The question of how much resources our medical system should invest into doing more autopsies however isn't trivial. It would raise health care costs if we give hospitals more money if they do more autopsies.
Maybe hospitals do have special genetic tests and reliably do those? But then isn't there going to be a pretty strong bias based on the fact that these are only for people who are getting hospitalized?
Hospitals aren't the only places that run tests besides at-home tests. The labs that do PCR testing retest some of the positive tests with variant-specific tests. Different countries have different policies about that.