GDP is not just a number you know. If one were previously hungry and cold and are now well fed and comfortable, of course that affects happiness. Why do you doubt that?
Wealth only really matters to the point where you can support a good living. That "good" will vary but beyond that increases in wealth bring diminished returns. Think about a salary: if it's below a threshold you are unhappy no matter what. Above that any raise brings more marginal increases in satisfaction, you start looking at other things for that.
The US is past that point so now it needs more than wealth.
GDP can be one marker for 'things are improving'. Of course it isn't the full picture - when you are living in increasingly restrictive state monitoring you against your own will, you feel the government is bunch of idiots, jobs have been shifting away and so on and on, people are not that happy. Rich are getting richer, poor poorer. If you are 2 joints away from serving prison sentence and having your life ruined for good (maybe less relevant these days).
Losing 'friends' around the world - 30 years ago, americans were heroes, WW2 saviors of the europe and the world, America was land of endless opportunities and most importantly - freedom. Now its the opposite - unlawful killing of somebody with tons of civilians with drones wherever they want, and in the same time being very friendly with horrible regimes like the one in Saudi Arabia because oil and money. Freedom and US ain't the same thing after 9/11.
Plus on top of that workaholic US mindset, that weird attitude that your job defines who you are and whats your position in society. None of this can make masses happy, in contrary.
Probably impossible to say, but I'd guess you'd have diminishing returns. So economic growth in a poor country will have much greater benefit than the same level of growth in a rich country.
Increase in GDP also brings very tangible improvements in income, life standards, modernization of cities, new technologies and a lot more to be happy with.
Tangible improvements for people who already have money.
GDP doesn't tell you where the money is going, and who benefits from it.
GDP may as well be a measure of how well the rich are doing because it tells you next to nothing about how the most disadvantaged in society are doing.