I've searched through the SOFTWARE\Classes and SOFTWARE\Microsoft subkeys, but couldn't find anything related to "spartan" or "edge". Given that Edge is still very new, there really isn't much information about this yet.
As an example, this is how I gather the information about the Internet Explorer Version via the registry on a remote machine:
$ieVersion=[Microsoft.Win32.RegistryKey]::OpenRemoteBaseKey('LocalMachine', $args[0]).OpenSubKey('SOFTWARE\Microsoft\Internet Explorer').GetValue('SvcVersion')
Use the Get-AppxPackage
command:
Get-AppxPackage -Name Microsoft.MicrosoftEdge | Foreach Version
The package name is valid on build 10240 but if you are on an earlier build, it might be different. If the above doesn't find the package try -Name *Edge*
or -Name *Spartan*
.