MBP 2012 recovery mode installs macOS 10.8, which can’t connect to much of anything any more.
10.15 is the latest that is compatible with the hardware. OK. Installer needs 10.9. Sigh.
10.9 installer can’t verify itself and refuses to run. FFS.
I guess I have to try going up each version in turn until one works?
All this to check if the battery works in macOS.
Apple. It Just Works.

