Wki has a good description of da (there) sein (to be). Heidegger didn’t invent the term (Hegel used it too) yet reinterpreted it. To be (or not to be vis. Shakespeare) seems self-evident .
Heidegger may have considered criticism of social existence in a way similar to that of Kierkegaard criticizing 19th century German romanticism that followed Hegel. Socratic irony considered the superficiality of social existence as did Kierkegaard who regarded Socrates as having created a method of social analysis critical of ‘inauthentic being’.
Heidegger was initially appointed Minister of German education by the Nazis yet quit fairly soon upon discovering what a bunch of louts they were. He retired to a hut in the forest to work on philosophical projects and had the opportunity to think about inauthentic social existence and group think (Orwell later) or what Sartre might call the social dialectic and Nazi use-truths.