How do the soliloquies in Hamlet create atmosphere?

Hamlet is a dark play with a mood of foreboding and death hovering in the air. The play opens on a foggy night with rumors of war and the frightening appearance of a ghost. Hamlet's seven soliloquies, which often deal with thoughts of suicide or death, reinforce the dark tone of the play, as well as the tone of deep introspection. This is not simply a revenge play, but a play that thinks deeply about the implications of revenge and death. Hamlet's soliloquies are key to getting us as an audience to slow down, stop, and think about what is going in Denmark's court. They also provide the audience with crucial information about why Hamlet is or is not taking action and offer insights into Hamlet's brooding.
For example, in the "to be or not to be" soliloquy, Hamlet makes clear how distressed he is about the situation the ghost has put him in—so much so that he wishes he were dead rather than having to face that his uncle might have killed his father. But the soliloquy also informs us of Hamlet's religious sensibilities: he fears what might happen to him after death were he to commit suicide. This helps us understand why he doesn't kill Claudius when he sees him as his prayers in Act III, scene 3: as Hamlet explains in this soliloquy, he doesn't want Claudius to die in a state of grace and go to heaven while his father haunts the earth as a ghost:

Now might I do it pat now he is praying,And now I'll do it, and so he goes to heaven.

Hamlet's soliloquy about not killing Claudius is also somewhat ironic, for we as an audience know that Claudius, though seemingly at his prayers, can't repent of his crimes and wouldn't have died in grace.
Hamlet's soliloquy about confronting his mother In Act III, scene 2, gives us crucial information. He says:

'Tis now the very witching time of night,When churchyards yawn, and hell itself breathes outContagion to this world...Soft! now to my mother...Let me be cruel, not unnatural;I will speak daggers to her, but use none

He tells us, his audience, that he will not try to kill her—he will only speak daggers, meaning speak sharply, but not use one. This too is ironic, because she could have benefitted from that information, which she doesn't have—she does think Hamlet is planning to kill her, which is why she cries out, leading to Polonius's death. However, the soliloquy is also important in continuing the mood of darkness and foreboding that permeates the play: Hamlet speaks of a "witching time of night," of "hell" and of "contagion." The mood shows the tenor of Hamlet's thoughts.