Update MacOS on a MacBook with dead battery
Well baring the obvious and replacing the bad battery you will probably have to install the OS on a different computer and reinstall the hard drive.  The Mac power module is not responding that the laptop is connected to AC but responding that the battery is bad.  Apple will replace the battery for $199 so keep that in mind while doing any work around.

You can also put this MacBook in USB target mode and run the installer from another Mac to perform the upgrade without fixing the hardware. The battery service there is relatively labor and parts expensive due to the thin assembly, delicate cabling and glue that makes the cells part of the case structure. You’re getting a partial frame replacement when the battery is exchanged for $200 and possibly new top case / keyboard if the cabling or parts don’t fit when it’s out for repair.