Results are different, often opposite, in countries that have a better relationship to meat, like the big Austrian food survey study from 2014: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3917888/
> Moreover, our results showed that a vegetarian diet is associated with poorer health (higher incidences of cancer, allergies, and mental health disorders), a higher need for health care, and poorer quality of life.
Other survey data across several countries often replicate the meatless = lower mental health claims, eg: https://www.tandfonline.com/doi/full/10.1080/10408398.2020.1...
(This should come as no surprise to people who have read about B12 and mental health, which is a relationship so extraordinary that I'm surprised its not more front-and-center.)
But again, food survey data is generally bad. Some are okay, when they are very focused, like the Swedish studies on dairy product consumption. But most of them are bad, and the more general, the worse they are.