A 2017 Freiburg study [1] took 36 moderately clinically depressed patients and assigned 17 to 30-minute, 40 °C hyperthermic baths, with 19 as control.
After bathing twice a week for four weeks, the study claims the 17 patients had a "moderate but significant improvement".
As someone who has suffered severe depression on more than one occasion, in those times I know I should practice good hygiene, nutrition, exercise, sleep habits, etc., but the very nature of depression is that it takes away the motivation to do those things. If I were in a study where someone actually prepared the bath for me at a spa center, I bet I would also improve.
IMO, "fixing" depression really means fixing fundamental self-motivation, not just a transitory "oh this feels a little better".
"In health care, self-care is any necessary human regulatory function which is under individual control, deliberate and self-initiated."
For n=1, I've struggled with (manic) depression and anxiety most of my life. And while I've used a variety of strategies to cope (Seligman's "Learned Optimism" and a potpourri of Buddhist ideas were incredibly helpful), the secret sauce was getting off of sugar and junk food. When I'm staying on a whole-foods, keto-ish diet, mood swings and unwanted negative thoughts have their volume is turned down by 90%, making the remainder relatively easy to process.
Everybody's different, so YMMV; in some cases, medication are an appropriate tool. But there are some universals that basically benefit every human: drink more water, get more sleep, go for a walk in the sunshine, eat your vegetables, and the less sugar (probably) the better.
All medical interventions should include the no-brainer diet, vitamins, exercise, self-esteem interventions.
That's a very strong claim to make so nonchalantly and confidently without referring to a source.
So this is really just 17 people assigned to take a warm bath. The thing about mental illness is that it's really really hard to be sure if something helped. You're brain is the thing that is broken, and your brain knows you are being treated.
I have depression. I've lost count of the things I've tried, and when asked, I have to say "I don't know if this actually helped or if it's just my brain thinking it should have helped."
With depression, studies which are not double-blind are garbage.