There are two topics here.
First, there is the question of whether Twitter and other social media should be an open place for people to hash out ideas about Covid. Here, my answer is: yes, it should be. But with a caveat--I think the fundamental principles of how a lot of social media works need to be at least tweaked first. Right now, to prevent bullying and abusive behavior, people get a right to silence each other--if I say something incredibly, horribly, maybe even dangerously wrong, and you correct me, all I need to do on Medium to eliminate your correction is to block you; on Quora I can delete your comment (!); on Twitter, their reply is still there, but I can always say the same thing again and now, since you can't see me, you can't reply; and so on. This is not like a public square because on a public square, I can't silence my critics. There is no necessity for ideas to be challenged; you can eliminate the challengers instead. That's not freedom of speech! So failing a fix to this that discriminates between disagreement and abuse, and only allows blocking in the latter case, I think soft moderation is a reasonable idea: at least in the most egregious cases, a flag that says, "this seems really wrong, go look here for another perspective" recovers rather than impedes freedom of speech.
If Twitter had only been doing that, there wouldn't be much of a problem.
The second topic is about Covid. You claimed that the vaccine was causing infection. That's not right. The virus causes infection. It is this completely wrong statement that I objected to.
Now you're saying that the vaccine is less effective than at times has been reported. That is true, and mostly isn't being hidden (though Twitter seems to have had some moderation misfires even there). The biggest factor is that public policy that was established for the case of recent inoculation with a well-targeted vaccine against a virus with low diversity is often being continued in the case of old inoculation with a less-well-targeted vaccine against a virus with considerably higher diversity. It's not that the old stuff was wrong, it's that the virus has mutated and diversified.
The value of free speech in this case one would hope would be positive. For example, you might learn that age- and health-matched controls still are a lot better off vaccinated than not, when it comes to serious health outcomes, even though when you vaccinate 90-95% of your elderly people and they're the ones who tend to have serious health outcomes, yes, most of your cases are among the vaccinated, because while the vaccines are protective they're not 20-fold protective (especially when we are still just distinguishing between "vaccinated" or at most "vaccinated and boosted" and not, vs. which booster and how long ago, etc.--unlike, say, measles which basically is a static target, Covid is a moving one, more like the flu (but hey, Covid vaccines still do better than flu vaccines)).
Regarding transmission, virologists were saying for months before the Pfizer/BioNTech and Moderna results were out that the vaccine probably wasn't going to stop the virus because it required too high a level of protectiveness (they were saying things like "it needs to be at least 50-60% to be useful, but far higher to stop the pandemic"). Then, shockingly, the results came out that it had that high level of protectiveness, and they switched to saying, "Hey, we can really stop transmission with this, because people aren't even catching it!" But then delta and omicron came out, which reduced the vaccine's effectiveness at preventing catching the virus; and people's antibody levels dropped (as was predicted early on), and together this meant that the level of protection went back to the level that virologists had been expecting before the initial mRNA results.
So, I am taking the stance that the vaccines do what they...actually...do. And the stance that there are multiple studies--the ones from Israel are particularly good, typically--that demonstrate what they do. Nobody should really be confused about this who wants to know what is going on, because that part of it is all plenty well out in the open. Nonetheless, one still finds fragmentary information that, taken in isolation, seems damning (but only because it's taken in isolation), such as what you've done here.
Regarding transmission, if you stop infection, you kinda have to reduce transmission. The "it stops transmission" thing is a necessary consequence of 90-95% reduction in infection. Recall that at the time to goal was to get something working as fast as possible that could stop people dying; the study was tailored to determine that as best it could as fast as it could so we could start distributing it if it actually worked.
It's very easy now to complain that different studies weren't done, but at the time people were complaining that things were already going too slow! Really, things were accelerated about as much as was possible while ensuring that (1) the vaccine is reasonably safe, and (2) it is reasonably effective, both of which were done. There have been lots of follow-up studies covering a variety of other things. Transmission is a particularly difficult thing to establish because we hate contact tracing, and we hate being placed in a controlled environment. So unsurprisingly, we don't have particularly high-quality direct data for that. People can measure proxies, like virus titers, and that shows pretty much what you would expect--when you have pretty good protection from infection at all, you also have reduced virus titers (e.g. https://www.nature.com/articles/s41591-022-01816-0); by the time the vaccine is no longer preventing infection, most people have similar ranges of viral loads too. (The mechanism of protection against hospitalization involves a different branch of the immune system than is responsible for preventing acute infection.)
Now, again, it is true that policy hasn't really kept up with the science. But it's not because the science was wrong or the policy was wrong. Policy is just slow to adapt to changing conditions.