I can't answer the question of why, nor do I wish to speculate (maybe someone else closer to the issue can tell us what happened), but thankfully it's not completely gone. It looks like the binaries have been reuploaded to NuGet by other developers, although note that none of the packages are official ones from Microsoft.
The following packages were uploaded by NuGet user aybe:
As usual, to install them:
Install-Package WindowsAPICodePack-Core
Install-Package WindowsAPICodePack-ExtendedLinguisticServices
Install-Package WindowsAPICodePack-Sensors
Install-Package WindowsAPICodePack-Shell
Install-Package WindowsAPICodePack-ShellExtensions