I had a Vivosport, I used the heart rate monitoring on Activity Only so I wouldn't have the green light on all the time. Now I have a Vivoactive 4, can I do the same? I don't see the option, just disabling it completely.

Recent Garmin models need to monitor the HR continuosly to record the average Resting HR, and the HR Variability, which are then used for proper calculation of Calories burn during activities, for stress level measuring, for detecting the anaerobic threshold, and for other purposes. The consumption of the sensor is also rather negligible, so turning it off makes no significant difference.