"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.
> it would just reduce the error bars.
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.
Unvaccinated is two groups that are wildly different:
Those who've had Covid and those who haven't. Depending on where you are, unvaccinated may be majority share recovered, in which case this is an incorrect statement:
> It's more uncommon to get symptomatic covid in vaccinated vs unvaccinated.