I've been looking for a way to automatically monitor battery level in my BT headphones. I found
an old thread where I learnt that it's on a To-Do list (and that the implementation is blocked due to bugs).
Digging further I stumbled upon
Home Assistant community thread that presented the name of Android intent "
android.bluetooth.device.action.BATTERY_LEVEL_CHANGED". That was it - quickly drafted flow with block "Broadcast receive" proved this approach to be working. The drawback is that battery level cannot be read on demand, only when the broadcast is sent. The good part is that this info is broadcast at the moment of connection of BT device, so as soon the headphones are connected Automate gets fresh info on the battery state (and hopefully on every subsequent change of battery level - didn't have the patience to wait for discharging to see how often the broadcasts are sent).
I hope this may be helpful to someone.