https://www.ncbi.nlm.nih.gov/pubmed/28093386
"Our results showed that overall, the use of Facebook was negatively associated with well-being."
Naturally, even if this study is accurate it isn't definitive; the causation could go in the other direction, that the unhappy use Facebook more often than the contented. But it's still quite suggestive.
I saw this study referenced from this article: https://www.vox.com/policy-and-politics/2018/3/21/17144748/c...