Beside maintaining physical health - sleep, exercise, hydration, nutrition, not too much alcohol, etc.; as well as conditions with clear etiology like schizophrenia; I strongly suspect most of the "mental health" stuff is BS, and the key is treating emotions as dumb and unimportant, and suppressing them/working around then. Kinda like DBT with "rational" vs "emotional" mind and "wise" mind in the middle, but taken to the next logical level - DBT identifies a bunch of problems with "emotional mind" and tries super hard to move you /towards/ "rational mind", just not all the way. It's telling that there's no therapy in existence that tries to move you in opposite direction - most people on the other end of the spectrum simply don't have issues. So, why not work to move all the way?
In this context, typical attitude of validating and accepting emotions is harmful. Again, DBT distinguishes "invalid" vs "unjustified" emotions, but I think it's hippy nonsense - it's good to explicitly reject and invalidate emotions. It's not easy for problem emotions, but it's good to practice.
In reality, emotions are like zits - they are things going on in your body that mean nothing or matter little 95-99% of the time. So, ignoring or suppressing them is usually the right approach (after checking for physical causes, again was with zits - did you forget to wash your face? did you forget to sleep enough?). Looking at people "anxious because they feel sad for no reason" or "feeling shame because they are irritable and might upset other people" or such circular patterns (mentioned, among others, by Frankl in Man's Search For Meaning, although he'd probably disagree with me on other stuff), I wonder how much of the nebulous mental health issues are due to a learned pattern of focusing on one's own moods and emotions as if they actually meant something, and even if this is made worse by typical therapy. I wonder if this is why self-reported mental illness in the US is increasing despite the increased use of therapy (and drugs, some of which definitely do something, making the increase even more damning).
I think the analogy with physical sensations is similar for positive emotions - taste of good coffee is, like zits, usually of little importance and has no meaning, but explicit mindfulness of it allows you to appreciate it more. Ditto if you feel curious / loving / amused / vigorous - mindfulness helps a lot to enhance these feelings.
For a more specific example, a "mental health issue" I have is that I quickly get angry at trifles (slow software, traffic, people wrong on the internet); people would point that out as an example of how I need a different, non-disdainful approach to emotions, but it's actually a counter-example - this is the only negative emotion I appear to take seriously.
So, a similar tactic - catching myself and explicitly thinking "this delay doesn't matter, I'm not in a hurry - the anger is an invalid emotion", or "I don't care what that person thinks, they have no effect on me - the irritation is an invalid emotion" works well, when I can actually catch myself.