Not specifically about TM, but there’s no doubt that many people find a meditation routine can be a major help in coping with depession. (Not sitting like this 🙂 )

https://www.health.harvard.edu/mind-and-mood/how-meditation-helps-with-depression?fbclid=IwAR2zZ65kEgJMhNwWuo6jy-ymHRZGzvTjv9BcTAI4Hnz9T_PcNdiYhMYzhrk