I dont know if there is a convention for polarity order on JST plug, but most Li-Po batteries you can purchase on-line have it reversed in comparison to the plug on the Arduino board. I came across this post Power an Arduino MKR ZERO by batteries and had the same experience with similar battery I purchased. In-built battery protection circuit stops battery from charging and because of reversed polarity Arduino protection stops it from powering the board.
What is misleading is that charging LED shows charging when there is none. So if you have trouble with the battery, make sure you double check Arduino board pinout as to where goes the + and the -. If your JST reversed, you can carefully lift up plastic hooks that hold in place JST terminals on the battery and pull out the terminals, swap around and reinsert.
After I did this the battery started charging (you can check it by printing analogRead(ADC_BATTERY)) in a loop, and after unplugging the power, board continued to run on battery power.