The term "shallow end" typically refers to the part of a swimming pool where the water is less deep, often designated for beginners or individuals who are not comfortable in deeper water. It is the area closest to the edge of the pool where the depth gradually increases towards the deeper end. In the given clue, "Sorry you're upset! Gotta run, late for my nail appointment," the term "shallow end" is used metaphorically to describe a comment that appears insincere or lacking depth. It implies that the speaker is avoiding a genuine conversation or disregarding the other person's feelings.
Note: The provided meaning of the answer is for the latest New York Times crossword puzzle clue: Comment like "Sorry you're upset! Gotta run, late for my nail appointment"?. Explanations are generated by AI and may be inaccurate.