......what would you do?....
My question would be 'what could you do?' and the answer is 'nothing'.
The B777 electrical system is completely automatic in operation and faults are detected and isolated without pilot action. The battery charger gets power from the ground service bus and in flight that bus is powered by the right main AC bus. To kill the the right main AC bus would require opening of the right bus tie breaker and selecting the right main and backup generators off. Would you seriously consider trying that without guidance of a non normal checklist?
Your B777 technical course should have emphasized that 'EICAS is king' . If it does not appear on EICAS there is nothing you should do. In flight status messages are advisory only and should not be a basis for unguided troubleshooting.
The main use of the battery is for initial power up and APU starting. If it fails or is isolated in flight it is of little consequence, given the multiple power sources available, even on a 3 hour single engine diversion.
I suggest you stop worrying and leave the system to look after itself.