I agree with this claim that heavy use of social media is linked to mental health issues, but to some degree. There isn't a direct casuality between social media and mental illness that we can prove, but for example, the according to Stanford law, the amount of major depressive episodes increased from 8.7% in 2005 to 11.3% in 2014. This is also the time frame social media came into our lives, implying the direct relation, but we can't confirm the statement.
https://law.stanford.edu/2024/05/20/social-media-addiction-and-mental-health-the-growing-concern-for-youth-well-being/
The source used was from Stanford Law which has high credibility because it comes from Stanford school while also gave a list of reference to show at the end of the article. The article was unbiased considering it gave facts rather than it being opinionated.
Overall, you cannot claim there is a direct relation between mental illness and social media use, but it can be implied that there is some sort of relationship between the two.