yes, plenty of studies of the effect on mental health. whether it's "definitive" is a matter of debate (and opinion). as a parent of teens/preteens, I 100% support this just like I support banning the sale of cigarettes to minors. And if future research definitively shows that social media is not generally harmful, then it can be allowed and no harm done -- meaning that it's not like the ban deprives them of some essential need.
It's not even so much the social media itself, but it's the companies controlling social media, who push every lever to try to increase engagement. It's not unlike the cigarette companies back in the day, trying to make them as addictive as possible, with ads everywhere, getting it movies so it's cool, etc.
If we had no-ads, paid subscription social media accounts, no endless scrolling, where social media companies revenue was not tied to time spent in the app, where you only see from people you follow, that would be a whole different conversation.
Meta/ByteDance/Snap/YouTube have f*ed it up, and this is why we can't have nice things.