It's very questionable that happiness can be measured or even desirable. The focus on positive emotions is easy and attractive, and yet human beings need a range of emotions to have a fulfilling life.
Like you said, happiness is a part of a fulfilling life, but it is not everything.
Happiness is also used in many other contexts and can include times of pain, crying, etc. Life satisfaction, flourishing, overall well-being.
One example I frequently mention is running. Running can be extremely painful, physically exhausting, and mentally draining. Yet runners will frequently describe their runs using word happiness. Why is that? Because there is more to happiness than just feeling good.
My parents were delighted with me ages 0-10. If you polled them again 10 years later, they'd have a very different response.