Whatever works for you. I avoid added fat as much as comfortably possible as only that works for me. But it’s great for others. And I didn’t even have breakfast on high-carb let alone on keto. We are different, we get hungry at different times, we have different tastes (BP coffee sounds not tasty at all to me), different goals and energy need (I can’t afford zillion calories for a drink)… There are almost zero strict rules. Drink a BP coffee if you want, whenever you want if that works for you just fine.
My not black coffee (far from BP, lower calorie and protein is involved) always happens in the afternoon, well, I normally only consume calories there so of course… It’s perfectly fine, even useful then.