The recent surge in violence as DAs have stopped fully prosecuting criminals -- including those who commit violent gun crimes -- has blurred the line between criminal violence and state violence. That renews the argument for self defense.
In other words, as the state declines to protect you, you have a better claim on the natural right to protect yourself.
I think the issue is that it's such an easy web-search, your failure to do it and instead make a "simple request" appears to present an implication that the phenomenon in question doesn't exist, i.e. gaslighting.
The assertion for which you asked evidence is not a correlation between prosecutorial policy ("fully prosecuting criminals") and crime rates, but rather the existence of the policies themselves. So, there's no need for a "study": the prosecutors put it down in writing (and those policies then get reported by the media).
For the record, I support some of these prosecutorial reform efforts, but through legislation which eliminates things like "add-on charges", not by prosecutors selectively deciding who will and won't get them.
But, since you asked, here's just a few -- and I'll make the "simple request" to you to do the "hard work" of a web-search if you want more than these: try Chesa Boudin, Larry Krasner, etc.
Manhattan DA Alvin Bragg announces he is directing his staff either not to prosecute, accept "community diversion" in lieu of prosecution, or at least not to seek any jail time, for a slew of offenses, including e.g. armed robbery:
And while anecdotal, here's evidence of the implementation of that policy, a letter from Union Pacific railroad to the DA's office, complaining that when their agents apprehend criminals robbing trains, they are not fully prosecuted:
I appreciate you taking the time to do this, explain that the existence of these policies itself is not in doubt, and clarify the difference between asking for proof of their existence versus proof of their effects on society. Because I had started to respond, but I decided it was bad for my mental state to engage further.
It sounds like you and I are actually quite close in belief that systemic reforms are necessary but that undertaking them by prosecutorial fiat is a mistake. You'd probably appreciate this analysis:
In other words, as the state declines to protect you, you have a better claim on the natural right to protect yourself.