This claim and article is well-based in reliable sources and multiple different perspectives. The information was sourced in the last 2-5 years from majorly credible sources. The first institution they refer to is a Wall Street Journal's research report, Facebook Knows Instagram Is Toxic for Teen Girls, Company Documents Show. This article displays a direct correlation between social media usage and declination in mental health with commentary and research from mental health professionals along with documentation from Facebook itself.
The other most notable source was a quote from the President and founder of Children and Screens, Dr. Pam Hurst-Della Pietra. Dr. Peitra has a BA from Cornell along with a MD in pediatrics from New York College of Osteopathic Medicine. Children and Screens is an organization focused solely on the impact of technology and media on children and their development. She says, "Social comparison, the pressure, the fear of missing out takes a hit on their self-esteem about their lives, their bodies, and their relationships.". This information backs their claim that social media has a direct impact on children's development and mental state.
The main problem with this claim is there is not enough information to directly correlate anxiety and depression diagnoses. While it is accurate to say that technology and social media have a large impact on development and social awarenesses, it is inaccurate to completely associate it with anxiety and depression.