I have this $13.50 BLE Temperature Humidity Sensor that advertizes the values every second. I measured average current is about 50uA. That's a bit too high current for indoor light harvesting with the two tiny solar cells, but you get the idea. If I would program the a BLE sensor I would make it advertise every 8 seconds to make it low power enough.
It is not a great idea to use the 3.3V output to power a device that is designed for 1x AAA battery. The AEM10941 harvesting IC also has a second regulated output voltage, which is 1.8V. That is lower power because it is efficiently stepped down from the battery voltage using a buck converter. In the next revision of the design I will break out the 1.8V output to the castellated via's