When I was in honeymoon phase, my endo explained that caffeine can (temporarily) inhibit beta cell production of insulin. I didn’t verify this in the medical literature but he’s a sharp guy and it explained a lot about how my morning BG levels were doing then. Now that I’m not producing much if any insulin things are actually easier to manage, and I use a fair bit of insulin in the morning just to cover life during that time of day, irrespective of any breakfast carbs. Who knows, maybe caffeine has other effects on the body’s morning/DP responses, but so long as I can balance those effects with insulin I’ll continue with my coffee and tea, hard to imagine a morning without!
Like @MarieB said, you can find a LOT more discussion about caffeine, and dawn phenomenon in other threads; here’s another one on coffee and morning responses - https://forum.tudiabetes.org/t/coffee-spiking