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.

10.12 installer was readily available from Apple and seems to be working better...

https://support.apple.com/en-us/102662

How to download and install macOS - Apple Support

Download and install current or previous versions of the Mac operating system on compatible Mac computers.

Apple Support
10.12 installed and connected to the App Store OK ... which allows me to run the 10.15 installer...
Progress…
I preferred macOS when it looked like this.
@nivrig snow leopard was peak