The second article also discusses the problem of the 2 week delay period and links to the study appendix - different data and argument.
Hospitalization is unfortunately also hopelessly confounded by the same factors - if you don't vaccinate people who are already dying then they are much more likely to be or end up in hospital - but then additional problems too. Again, RCT data didn't prove any effects on hospitalization, that just wasn't an end point they cared about.
Why not? Well, partly because it's extremely subjective. To be hospitalized for a disease like COVID you must either catch it in hospital, or choose to go. COVID isn't a sudden collapse like a heart attack or stroke where bystanders may rush you to hospital in an ambulance. It's a steady degradation and at some point someone has to call a doctor or emergency number and say, I think I need to go to the hospital. Hospitals can turn you away if your COVID isn't serious enough but in many places they have monetary incentives not to do so, and that's ignoring all the psychological issues - if you have some spare beds giving someone who's terrified some attention may be better than turning them away.
In normal/sane times this wouldn't really matter, as we can hope that people are roughly OK at judging whether they need this or not, and hospitals wouldn't spend resources on cases that aren't really needing to be there. But with COVID, years of relentless misinformation from newspapers and authority figures have totally destroyed people's understanding of the severity of the disease. US adults over-estimate the risk of hospitalization if you're unvaccinated by orders of magnitude:
https://news.gallup.com/opinion/gallup/354938/adults-estimat...
"The results show that most Americans overstate the risk of hospitalization for both groups: 92% overstate the risk that unvaccinated people will be hospitalized, and 62% overstate the risk for vaccinated people .... For unvaccinated hospitalization risk, 2% of Democrats responded correctly, compared with 16% of Republicans. In fact, 41% of Democrats replied that at least 50% of unvaccinated people have been hospitalized due to COVID-19."
41% of left leaning voters think HALF of unvaccinated people have been hospitalized for COVID! The true number is less than 1%. That's an astonishing stat. I suspect these polls aren't representative and the true numbers are better than this but even so, they are indicative of the problem.
What happens if you trust the media and government so much that you're totally convinced testing positive for COVID = required hospital visit, and then those same authority figures tell you that vaccines will "protect" you from hospitalization? Well, you're much less likely to go, even in situations where previously you would have gone straight to the ER and demanded attention. And that's fine, they'll recover on their own as they almost certainly would have done anyway, and they'll say "thank god I was vaccinated otherwise it would have been much worse".
This is the sort of confounder a rigorous trial would seek to control for, but we don't have any useful trials. The vaccine trials were complete failures: for the only end point they targeted, they reported 95% effectiveness, which started dwindling to near or even below zero in the months after the trial period ended. No usefully accurate information was provided by them, which is shocking.