"rates among unvaccinated persons with a previous COVID-19 diagnosis were 29-fold lower (95% CI = 25.0–33.1) than rates among unvaccinated persons without a previous COVID-19 diagnosis in California and 14.7-fold lower (95% CI = 12.6–16.9) in New York. Rates among vaccinated persons who had had COVID-19 were 32.5-fold lower (95% CI = 27.5–37.6) than rates among unvaccinated persons without a previous COVID-19 diagnosis in California and 19.8-fold lower (95% CI = 16.2–23.5) in New York."
Asking for a "significant" difference is just using weasel words to note that each individual post-Delta study is not powered to detect a difference with those very small slices and no metanalysis having been completed yet. Every single study has shown a point estimate difference that is consistent with vaccination conferring additional protection on those who have previously recovered.
I'm using the term correctly and whether the numbers combine to indicate technical statistical difference won't impact that small difference, it would just reduce the error bars. Taking new york high end vaccine effectiveness 23.5x and worst case natural immunity 12.6x you reduce your hazard ratio by factor of 2. That is absolute worst case for natural immunity and best case for vaccine. It will be a lot closer to 1 perhaps 1.2x. Now compare that to you worst case baseline reduction of 12.6x already and how much more do you have to gain? Are you for all practical purposes protected enough?
Significance is about the error bars. You are not using the term correctly.
The statement that you originally claimed to be incorrect remains true. It did not make any value judgments about whether a group is immune enough. It only made a factual claim that one group is less likely to get a symptomatic infection than another.
