A cup of black coffee contains about 1g of carbs - maybe 2g depending on the type/amount of coffee. Even at 3-4 cups per day, you’re talking maybe 5g of carbs and 20 or so calories.

Does this ‘break’ a fast? Probably depends on how sharply you define a ‘fast’. Are you going to break it, as in totally sandbag all the benefits of it? I doubt it. One of the objectives of fasting is to deplete your glucose so you can run on ketones - 20 or 30 calories is not going to be enough to replenish that (at least, I couldn’t imagine it would be; I’d say it’s a safe assumption unless either of them explicitly refute it