I think emotional health and mental health are different.
Resilience has nothing to do with mental health. Many kids with poor mental health have amazing resilience.
I think both these are true, which is why I feel I still have something to contribute to this thread even though my eldest has had poor mental health since childhood (hereditary in our family).
She does however have enormous resilience. I would say also very good emotional health, in the sense that she is level-headed, very good at distinguishing between the symptoms of her illness and actual injustice/hardships, has a great sense of humour and very good social skills. She is good at spotting abusive behaviour and also has high standards for her own behaviour.
I am very glad of that as it seems to me that those are the things that we might to some extent have been able to influence as parents.
Reliable adults to talk to and parents reacting predictably has been mentioned above, and I think those are very important.
Team sports have not been possible- a child who is sometimes in a wheelchair and sometimes able to dance doesn't really fit in anywhere in the world of sports- but youth theatre has filled the same function.
Not catastrophising has been particularly important as some pretty grim things have happened. Modelling calm and self control, at the same time as openness, has made a big difference. If things are difficult, knowing that your parents are tough enough that you don't have to spare them makes a big difference.
Also staying calm in the face of perceived injustices and not encouraging hard-done-by attitudes. (Youth theatre is really helpful for this, as there will always be somebody who gets cast in the role your offspring thinks they should have had)
Encourage independence definitely, and not only in practical things but also by helping them work through their relationships and other problems, listening and asking what they think might work best rather than telling them. Sharing strategies, as someone said earlier, rather than trying to sort things out.