In the given sentence, “Warum sagen Sie denn nichts?”, the word “denn” is a modal particle that adds emphasis or emotion to the sentence. It can be translated to “then” in English. Modal particles are common in German and are used to convey the speaker’s attitude or mood. In this case, “denn” adds a sense of urgency or impatience to the question. The sentence can be translated to “Why aren’t you saying anything then?”.
Your understanding of the German sentence is very good.
However, I am not completely convinced by the translation with “…, then.” in the end.
That sounds to me more like
"Warum sagen Sie dann nichts?
Maybe
“But please, why aren’t you saying anything?”
Or even
Why for heaven’s sake aren’t you saying anything?"
But then (pun intended) I am not a native speaker.