DFRobot still didn't aswer my question. Neither here nor in the FAQ on the product page. 

Fortunately another person, shadeBlue, found the solution. It seems that for unknown reasons the board has two unpopulated pads which can be bridged to make it work as expected. If someone's interested, please see the shadeBlue's answer to my thread in the product page: https://www.dfrobot.com/product-1590.html

I have no idea why the board is designed this way. The solution seems to work and unless DFRobot finally decides to tell us something, bridging those pads looks like a way to make the voltage reading work.

Hello. Is this forum active? Could someone from DFRobot please answer my question?

Somehow half of my post didn't show, here's the rest:

The A0 pin is indeed connected to the ESP32's pin 4, but when I connect a battery, the A0 pin is floating (as measured with voltmeter) and the adc1_get_raw() returns 0.

Isn't the voltage divider connected to the A0 pin? Is it connected somewhere else? How do I measure the battery voltage?