From the report: "One in six young people will experience an anxiety disorder at some point in their lives and
identified rates of anxiety and depression in young people have increased by 70% over the past
25 years. Our own research has shown that young people themselves say four of the five most
used social media platforms actually make their feelings of anxiety worse (See YHM survey - page 18)" [my emphasis ]
But you're right insofar as this doesn't appear to be a longitudinal study with a control group. But such a study would probably be pretty hard to pull off.
Maybe ESS[1] could help here if questions about social media habits were added - but we'd not see results until a few years hence, obviously.