Others have pointed out that most of the factors you take into account are (often strongly) correlated with GDP per capita. What I think is more important from an econometric perspective is that many of them are caused by GDP per capita. If you’re trying to measure the effect of (average) income on happiness, and you control for almost all the mediators of income’s effect on happiness, of course you’ll find that there is almost no independent effect of income left over!
In my opinion, this analysis, while certainly interesting and useful for other purposes, says nothing at all about the effect of GDP per capita on life satisfaction or happiness.
The factors being only caused by GDP is not at all central to my argument against your analysis, nor is it a claim I would make. The key point is that any causal effect of GDP on happiness must necessarily run through other factors like shelter, clean water, health, etc. Nobody (except economists like me) feels more satisfied with their life as a result of hearing that GDP/cap has gone up by 3% this year.
As such, if you control for all of those mediating factors, it will be literally impossible to find a significant effect of GDP/cap on happiness whether or not such an effect actually exists. If the effect is real, such an analysis would necessarily find a false negative.
Similarly, your counterexample would be valid, if I were claiming that GDP is the only factor in happiness. Again, I do not claim that, nor does anyone I know of. There are plenty of factors which account for national average life satisfaction, one of which is GDP. It is perfectly possible for Costa Rica to be higher in other factors and therefore be happier than the US despite a lower GDP.
There are some economists who oppose GDP as a measure of value, and some who support it. If you’re appealing to expertise, there’s a huge difference between consensus view and “some experts agree with me”.