The problem I see is that there is no institutionalized way to educate about emotions. For abstract knowledge and training rational thinking we have schools and universities. For feelings/emotions, though, we were are all effecively just getting homeschooled: We can learn from our parents etc., but that's pretty much it.
Perhaps there should be something like a school for feelings. This obviously is a hot topic, though, with different cultures having different ideals etc., especially when it comes to things like purpose in live, like we could already experience in another thread :)
I find one of the fundamental ones is pain. It's not an emotion, but it's not that easy to classify what is actually painful and what isn't. Holding a phone in my hand isn't painful, but at some point I managed to do it so much that it did become painful. I don't know how to describe the pain, but I know that I am apprehensive of holding a phone in my hand for extended periods of time.
Another one is stress. People might not know they are stressed, but they are. They just can't recognize what stress is.
What I'm getting at is that a lot of things aren't taught explicitly. We don't even know how to teach some of that, because we don't have a good classification system for the feeling/emotion.
What I mostly meant was similar to your stress example. Many people don't actually know what stress is, how it manifests, and most importantly, what you can do about it. Many also don't know that people can have very different thresholds of tolerable amounts of stress, and that those thresholds can siginificantly differ for the same person doing different kinds of work/studying etc. (e.g. some people have very low tolerances for arguing/discussions in work groups but can effortlessly dig themselves into research for 8 hours, others can do meeting marathons but have problems with physical work affecting their mood and so on).
In these cases many aspects of both the basic knowledge, ways of prevention and methods of coping with stress are well known, they just aren't taught in regular school. There is slow progress, though. In my country there often are e.g. social pedagogues in primary and secondary schools, helping with these kinds of things - though often only when they already manifest themselves as problematic behaviour.