Managed high BP. Healthy diet. Exercise regularly - HIIT. Prediabetic. Cholesterol borderline. Why heart rate increase rapidly after a short day nap?

Heart rate is. regulated under autonomic control and function. Aging, glucose intolerance, medications, physical condition and hydration can all have effects on the autonomic system resulting in variability to the heart rate response to various activities. Sleeping can additionally affect the autonomic responses. I suspect this is normal physiology for you and represents your body's response to these factors.
Uncertain . With your history one of the causes could be hypoglycemia. You might check to see what time of day you have a nap and whether it correlates with your sugar.