See section 6[0] where they discuss how mental health declines correlating with Facebook coming to college campuses and with high speed internet arriving in cities for some evidence.
[0] https://jonathanhaidt.substack.com/p/social-media-mental-ill...
This stat can't be meaningfully compared to teen suicide rates because the latter is across all teens, regardless of online/offline status. If the number of "online" teens grew dramatically between 2006 and 2013 (as I suspect it did), then the relative change in percentage of "online" teens on social media would be much smaller than the change in teens in general.
My personal experience growing up around then is that a majority of my peers weren't deep in social media and smartphone use until well into the 2010s. I didn't have a smartphone when I graduated high school in the early 2010s, and I certainly wasn't an outlier at the time.
Among adults (or in “household” surveys where adults were surveyed? Sure, but the majority of teen internet users were using “social networking sites” in 2006.) [0]
If your contention is that adult social media use is driving teen suicide rates…well, that’s actually more plausible than teen use, but none of the policy responses address that.
[0] https://www.pewresearch.org/internet/2013/05/21/part-1-teens...