>The evidence linking diet and depression is really very limited.

I’d say the opposite is true there are many available studies on dietary inflammation (ie chronic inflammation) and depression being linked.

See the inflammatory hypothesis of depression, also interesting is data is beginning to reveal a link between inflammation and the 1/3 of patients who do not respond to antidepressant medications. Generally when working antidepressants have an anti inflammatory effects.

It should also be noted that the diets mentioned Keto/carnivore/vegan all generally emphasize the removal of inflammatory foods (ie refined sugars, refined carbs, fried foods, artificial trans fats, etc...).