This seems to be the study: https://jamanetwork.com/journals/jama/fullarticle/2787447
Vaccinated people with Delta infection got new antibodies especially against Delta. That's good news. There was a possibility that vaccinated people always react with the same set of antibodies, so they will get re-infected again and again.
To gain immunity against a particular infection doesn't really mean anything, just that your immune system is working as it should.
The shots were supposed to protect against that to start with - that's the interesting part. They didn't.
That the shots don't affect Delta (identical virus load in vaccinated and unvaccinated) is very old news. The new news is that there seems to be no wide spread original antigenic sin (https://infogalactic.com/info/Original_antigenic_sin).
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