Does black coffee break a fast?
No. Black coffee has around 2 calories a cup and does not break a fast. Milk, cream, sugar and syrups do.
Black coffee is close enough to calorie-free that it leaves a fasted state alone. This is why it is the single most common thing people drink during a fasting window.
The additions are what matter, and the line is less obvious than it looks. A splash of milk, a spoon of sugar, oat milk, flavoured syrup and most "skinny" versions all carry enough to count. Bulletproof-style coffee with butter or MCT oil very clearly does: it is a meaningful number of calories, whatever the marketing says about ketosis.
One honest caveat that is not about fasting at all. Coffee on a completely empty stomach makes some people jittery or nauseous, and that is worse in a long fast when you have had no food for many hours. If that is you, it is not a moral failing to move it into your eating window.
General information, not medical advice. Intermittent fasting is not right for everyone. Talk to a clinician before starting if you are pregnant or breastfeeding, have or have had an eating disorder, have diabetes, or take prescription medication.