It's risky to describe the claims of social studies profs as clear empirical evidence, given the history of the field.
Twenge makes some unscientific arguments in her blog post, like constantly conflating correlation with causation despite her evidence not being able to show that. She also seems to think that if she knocks down a series of counter-arguments, then that means that her own argument must be correct. Given that Haidt's identical claims already turned out to be based on very poor quality evidence [1], their argumentation must be examined carefully before rushing to action.
Still, assume for a moment that it's a correct causal inference despite the major flaws in their evidence base. There's another tricky aspect to this. The Twenge/Haidt argument is really only about teenage girls. Although Haidt is basically honest about this (see [2]), Twenge is not. The opening of her article you cite talks about teenagers in general, but the first figure only shows data for girls and women. Then the second figure is even captioned "Figure 2: tech adoption, teen depression" but the legend actually says "Depression, girls". A few paragraphs later she's making claims about "individuals" whilst providing evidence that's once again specific to teenage girls. Her article is full of sloppy conflations like this.
Anyway, needless to say, neither politicians nor academics are willing to only ban social media for girls. This would upset the left so the argument morphs seamlessly into "social media should be banned for all teenagers" which isn't a story found in their data. This punishes boys for the mental health problems of girls, but is that just?
There's also a more subtle logical problem with this argument. It assumes that teenagers are a fixed group, and thus any change in their behavior must be due to some immediate alteration to their environment. But it's not: "teenage" is a sliding window that people constantly pass through. In other words it's possible that these depressed teens have always been somehow messed up, and simply aged into the categorization they're looking at. By implication the true answer could be found in earlier periods, even as far as back as changes to childrearing practices in the late 80s/early 90s rather than something that changed specifically in 2012. One theory posits that it's something to do with the rise of extremely early daycare for infants (e.g. for children less than one or two years old), and they also have a variety of correlations to bolster their case.
It may be that social studies academics simply cannot answer such questions.
[1] https://reason.com/2023/03/29/the-statistically-flawed-evide... "Haidt's compendium of research does point to one important finding: Because these studies have failed to produce a single strong effect, social media likely isn't a major cause of teen depression. A strong result might explain at least 10 percent or 20 percent of the variation in depression rates by difference in social media use, but the cited studies typically claim to explain 1 percent or 2 percent or less. These levels of correlations can always be found even among totally unrelated variables in observational social science studies. Moreover the studies do not find the same or similar correlations, their conclusions are all over the map."
[2] https://www.afterbabel.com/p/social-media-mental-illness-epi...