This does not increase insulin levels. Metabolizing drugs is nothing like metabolizing calories. These increase stress and calorie consumption on the body, and do nothing to increase insulin and reset the body into storage mode.
In fact coffee, even decaffeinated increase autophagy. Furthermore, fasting for fat burning is not significantly decreased by consuming coffee with butter or oil added because these fats do not increase insulin. They do however feed the gut, so do break a fast for gut regeneration.
https://www.zerofasting.com/will-it-break-my-fast/
https://2mealday.com/article/what-breaks-your-fast/#:~:text=In%20short%2C%20anything%20that%20contains,what%20they%20are%20talking%20about.