But perhaps the cause-effect relationship is inverted - perhaps generally happier people tend to think free will exists, because they never had a reason to doubt it? In contrast, people who are generally unhappier are the ones who are thinking about topics such as free will, determinism, etc. to try to make sense of the world. Sometimes it works, and makes them less unhappy - but they had to be unhappy in the first place to start thinking about it.
But perhaps the cause-effect relationship is inverted - perhaps generally happier people tend to think free will exists, because they never had a reason to doubt it? In contrast, people who are generally unhappier are the ones who are thinking about topics such as free will, determinism, etc. to try to make sense of the world. Sometimes it works, and makes them less unhappy - but they had to be unhappy in the first place to start thinking about it.