OMG ! On re-reading the datasheet for this DFR0559 I just found something hidden away which I think should be significant.
I expect you noticed the regulated 5V header pins, and read that you can use the blue GND and EN pins to turn on/off the regulated 5V pins. Nowhere in the documentation is the BAT pin defined or even mentioned.
Way down at the bottom of the document is a section headed “Build a low power environment monitor station” with a diagram and explanation of providing 5V power and GND to sensors from these regulated pins rather than in the i2c cables. Given that my ESP32 powers off when in deep sleep, and hence is no longer powering i2c … it seemed rather pointless to complicate the wiring this way.
But tucked away is the innocuous looking comment “Use the analog input A1 to monitor the battery voltage (equivalently the battery capacity)” and in the wiring diagram that we see the Arduino A1 is connected to the Sunflower’s BAT pin. And yes, a multimeter across those pins reveals the battery voltage.
Maybe my interpretation is wrong, but it seems like the blue GND and BAT pins are designed to provide a way for the microcontroller to monitor battery voltage. So why would DFRobot hide this information instead of making it a feature ???
… now back to the drawing board to see how much circuitry needed to detect the battery voltage I can remove 
