The CDC prison study says "The attack rate was higher among unvaccinated versus fully vaccinated persons (39 of 42, 93% versus 129 of 185, 70%; p = 0.002)."
The Eurosurveillance article you posted says "The calculated attack rate among all exposed patients and staff was 10.6% (16/151) for staff and 23.7% (23/97) for patients, in a population with 96.2% vaccination rate (238 vaccinated/248 exposed individuals)." Do you think that indicates that vaccines don't reduce spread? What do you think the attack rate would be in an unvaccinated population?
The European Journal of Epidemiology article isn't actually trying to look at vaccine effectiveness in reducing spread. It has some interesting information, but that's not what it's about.
That study cannot be used to disprove the idea that the unvaccinated inmates all gave the virus to the vaccinated ones. That is almost certainly wrong and there should have been some onwards transmission from the vaccinated, but that sentence is quite literally correct. The study says nothing about it.
Meanwhile I've posted elsewhere:
The impact of SARS-CoV-2 vaccination on Alpha & Delta variant transmission
https://www.medrxiv.org/content/10.1101/2021.09.28.21264260v...
That study is real world contact tracing.
More so if the argument is that the hospital patient population is especially vulnerable.
We don't even know if the likelihood of transmission is reduced enough to affect over number of transmissions.
Another example of a major outbreak in a 96% vaccinated and high PPE setting: https://www.eurosurveillance.org/content/10.2807/1560-7917.E...
No relationship between case rates and vaccination across 68 countries: https://link.springer.com/article/10.1007/s10654-021-00808-7