Rather than building immunity we are accruing damage and the evidence underpinning it from the VA study and the more recent ones is massive.
Large numbers in a study is good, but if the study design isn't right, then large numbers won't make up for that. It's absurdly hard to really conclude reliably.
For example, from: https://www.nytimes.com/2023/08/17/well/live/covid-reinfecti... """For many people who get Covid multiple times, subsequent infections will be as mild as or milder than their first, emerging data shows, likely because of partial immunity from previous infections, vaccination and the fact that the latest circulating variants generally cause less severe symptoms.""" which is much more consistent with my understanding of COVID repeat infections.
If you have a link to the VA study I will look at it.