Aside is a theatrical term that refers to a line spoken by a character on stage intended for the audience to hear, but not the other characters on stage. It is usually delivered in a lower volume than the character's normal dialogue and is often used to provide insight, commentary, or reveal the character's true thoughts and feelings. The term "Many a stage whisper" is a clue suggesting that "aside" is related to whispered comments made during a play.
Note: The provided meaning of the answer is for the latest New York Times crossword puzzle clue: Digression of sorts. Explanations are generated by AI and may be inaccurate.