How could they be happy, being watched, judged, and probably condemned "for eternity" because of innate drives?!

Oh, I've definitely known content / happy people who happen to be devoutly religious. I can think of several examples. Since religious / god beliefs aren't a necessary ingredient for happiness (or unhappiness for that matter), there's no particular correlation that I can see. Sure, religion, especially authoritarian / fundamentalist religion, can tend to cause guilt, shame, self-loathing, delusions of grandeur, and probably chilblaines for all I know, it doesn't always do that. I come out of fundamentalism, and my parent's unconditional love and stable home life unintentionally inoculated me against the self-loathing and condemnation stuff. Of course they came to fundamentalism very late in life, and their character had not been sufficiently eroded by their ideology to cause me problems. And there were other ways religion harmed me and contributed to unhappiness in my life, mostly by setting wildly unrealistic expectations of how life operated and what I could expect from it.

People respond to their faiths differently, according to their own personality, proclivities, needs, strengths and weaknesses. My late wife had an aunt and uncle who really transcended their rural Methodist affiliations, did tremendous good works in the community, and were beloved by literally everyone who knew them. They were "pillars of the church", and in an unofficial sense, the very core of the church community, the sort of people you went to for wise, non-judgmental advice when you knew the asshat pastor assigned by the denomination would be useless.

These are really "exceptions that prove the rule" you're trying to put forth, of course. I'm not suggesting religion puts more net happiness into the world or something. I'm just saying it's not all equally toxic and doesn't effect everyone the same.

Since Belief and Happiness cannot be quantified on a general level (we each have our own definitions)being the same for all people I cannot see any correlation being made on a Scientific level.

They would not need to "believe" if they were happy.

I disagree . I know plenty if not all believers who are very happy in their world . I think " ignorance is blessing " indeed . The less they know and chose to know , the happier they are . A happiness that I do not envy however ?
Funny fact / timing as well , my client few days ago , a man on his late sixties , a priest . I will like to mention , not a single significant wrinkle on his face , and his hands softer than fine cotton . Some interpreted that as " oh the peace of godliness, the harmony reflects on his face . Aawwww".
I interpreted this as " lazy human who never had a real job or real worries . The check will come regardless , the product sells regardless , and the competition / job security is irrelevant ". Yeah , I ll be happy too ?

Whether you're a believer or not, it seems to me that there are plenty of reasons out there to be worried and unhappy these days and that you need to make quite an effort to go to what makes you happy.