The toolbox tool will be running as SYSTEM and as this is an AppX Package is likely tied to the user themselves, so it isn’t seeing the package under SYSTEM and taking no action.
If you use this syntax:
Get-AppxPackage -allusers Microsoft.SkypeApp_126.96.36.199_x86__kzf8qxf38zg5c | Remove-AppxPackage
This should hopefully do the trick. One suggestion I’d have is maybe to change it to:
Get-AppxPackage -allusers *SkypeApp* | Remove-AppxPackage
Then this would cover you for future use cases, as the PackageFullName will likely change in the future or an outdated version is installed on a system.