William Parry’s program “Valsalva Stuttering Therapy” has the best explanation for this in my opinion. As a person who stutters and an SLP, it’s the program I have had the most personal success with and the one I believe in the most. In the program we treat stuttering as a voice problem, primarily an inability to phonate the vowel sounds of words. Therefore the reason you don’t stutter when you sing is because the air is flowing, your voice is turned on the whole time, and you are focusing on melody. You don’t stutter when speaking in an accent because you are concentrating on your voice and melody again to match the accent you are mimicking. You don’t stutter when you whisper or when silently mouthing words because there is no voice involved. We also talk a lot about beliefs and expectation about speech, which explains why people don’t stutter/stutter less when talking to themselves, children or pets. It has to do with fear of judgement and so on. There’s a lot to it. Here’s a link that explains some of the nuts and bolts of the program. It’s kind of old but please watch the whole thing. https://youtu.be/Clmre6U8Rmg