It probably depends a lot on what the bite consists of and how fat adapted you are and your reasons for fasting. A bite of something very carby is worse than broccoli or heavy cream. If you’re fasting for weight loss or insulin control, I really don’t think a little cream or whatever is going to make much of a difference. For autophagy, I don’t think science really knows that much about how it works in the human body. They say protein will stop it, but for how long and to what degree?
You can find more technical detail by looking into mtor and AMPK. The digestive system seems to take two days to stop at which point some significant changes occur. I’m not sure if eating a small amount would restart digestion and take another two days to stop. I do know that even a small amount of artificial sweeteners from gum is enough to cause a major reaction while fasting.
There’s a whole lab researching exactly this for about 10 years now. Look up Walter Longo’s work.
Edit: One thing I thought was interesting was somebody recently asked him this kind of question on a podcast and he flipped it around and explained they are actually finding specific nutrients that make fasts do better things that pure fasts… as in improve autophagy or prevent certain muscle loss (really important for people above 40 who are very unlikely to get back any lost muscle).