My experience is that 30 mins of vigorous exercise at least 3 days per week has huge benefits on overall wellbeing - including mental health. The caveat there is that diet has to be tuned to support your level of activity. If you are exercising and not eating enough, low blood sugar can bring on the bad feels / thoughts.
Took me a while to realize that diet was the culprit; but after a lot of self experimentation I am 100 percent certain.
I'd also bet that it synergises well with yoga, as yoga is a decent mechanism for encouraging blood flow throughout the body.
I love lifting and think there are some really great elements. While ego lifting is bad, lifting a number is such a strong personal development feedback loop for most people but it's not for everyone: my partner is scared to get big, my mum and brother currently are nursing various MSK issues and can't really lift safely without serious modifications that need supervision. Meanwhile yoga, or better baduanjin (qigong) are far more accessible systems and bikram is a nice way to passively introduce extra challenge to the body and mind.
I suspect hot yoga would still produce comparably better results.
The reason is that it doesn't include only moving body around but things like breathing, stretching, compression, intense sweating etc on top of intensive workout. It gives subjective impression of positively affecting organs, lymphatic system, skin, hair, mind, circulation etc. - the whole body basically.
In the lifting world there's a common meme that goes something like "moving heavy thing make sad voice go away".