Putting a scope on the CS line with battery connected to the charger, I can see some communication. It seems that the charger has a pull-up to 5V on his CS pin, and the battery generate the data with an open collector (or open drain) output.

About the data itself:

The frame seems constant and identical on my two 8Ah batteries. It is this a repeated sequence (about 4Hz). 

Bit rate is 1kHz. At first I was thinking UART, but the stop bit doesn't match any 5-9 bits words with or without parity.

For now this is how I interpret the data: The battery says it can be charged, maybe specifying the current depending on the battery model,  cell balancing state, temperature etc, but it doesn't seems to include sensor data itself.

The charger do not respond back anything. I've included a 4.7kHz in series with the CS connection to confirm the data is only set low by the battery. This allowed me also to determine that the pullup value is about 7 kOhm.

Something very useful to remember: When the charger is plugged, the Bluetooth is awakened. This might come handy if we decide to implement the under voltage protection via bluetooth.