This discussion skips any consideration of the underlying premise that "self-reported happiness" is always significant

Populations in different countries often have very different pyschologies and societal customs, including propensity or reluctance to be outspoken, to express "feelings", to complain, etc. Populations may differ in how they respond to questions about "happiness"

For example, a country with relatively high "self-reported happiness" may also have a relatively high rate of suicide

If a "happy" population is the objective, then there may be more to examine than simply "self-reported happiness"

how would you measure "happiness" if you were tasked to do so for a study?

Sure, but this whole thing is about trends over time, so the societal customs shouldn't change drastically in a specific country in such a short time.