One key element is the 1950s - style setting which gives a sense of nostalgia but also hides the secrets well. Another is the character of Alice who is the one to question the status quo. And the mystery of the men's work in the community is also crucial.
The original story of 'Dont Worry Darling' is centered around a 1950s - style utopian community. The main character, Alice, starts to suspect that there are some dark secrets beneath the idyllic facade of the community where she lives with her husband. As she delves deeper, she discovers things that challenge the seemingly perfect world they are in.
It could also be that 'darking' is an action or an event that seems a bit ominous. But the story is meant to convey that one should not worry even when this 'darking' event occurs. For example, if 'darking' is like a dark cloud coming over a village in the story, the characters learn not to worry and find ways to deal with it.
Since I'm not familiar with 'dont worry darking story', it could be a story created by an individual or a small group. It might involve themes like facing one's fears, as the 'darking' could imply something a bit scary or unknown. And the 'dont worry' part would then be the advice or the conclusion of the story, to not let those fears or unknowns cause distress.
Well, Don't Worry Darling doesn't have a clear basis in an established story. It might draw inspiration from various themes and concepts, but not from a single identifiable source.