Which I didn't quite achieve ...
To create that I added two new registry keys to BgInfo:
HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Microsoft\Windows NT\CurrentVersion\ReleaseId
which I called OS Release ID, and
HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Microsoft\Windows
NT\CurrentVersion\BuildLabEx
which I named OS Detail.
I added those to BgInfo as
OS
Detail
<OS Release ID> <OS Build Version>
Then refreshed the desktop as in my previous post.