Amber O'Hearn is a famous personality and researcher in this space, there are a few accounts of her successful remission from bipolar type 2 with this regimen.
I can give other references and answer any related questions.
[Edit] I'm not aware of any science on all-meat diets and mental health, but there is scientific evidence supporting the role of nutrients in animal foods and brain health, as well as ketogenic metabolism VS glucose metabolism (notably as a treatment for epileptic seizures). Obviously what's good in calming epileptic brains is going to be good for calming all brains.
(Edit: studies associated) https://scholar.google.com/scholar?q=exercise+effect+on+depr...
Due to my severity, insomnia (primary), and psychosis, I will likely always need medication but taking care of my body allows me to keep the dosages low enough that I still feel like myself.
In general, taking care of yourself physically (beyond sleep and exercise this includes things like taking showers, brushing teeth, etc., which can be difficult during a slump) makes it easier to take care of yourself mentally since you have more energy and don't need to deal with body problems.
In my experience this stuff is helpful, but not a silver bullet.