Below is the answer to read anonymous and windows authentication:
$anonAuthFilter = "/system.WebServer/security/authentication/AnonymousAuthentication"
$windowsAuthFilter = "/system.WebServer/security/authentication/windowsAuthentication"
$value = 'false'
$AppName = "test"
$anonAuth = Get-WebConfigurationProperty -filter $anonAuthFilter -name Enabled -location $AppName
Write-Host $anonAuth.Value
$winAuth = Get-WebConfigurationProperty -filter $windowsAuthFilter -name Enabled -location $AppName
Write-Host $winAuth.Value
@Peter Hahndorf
Still didn't find any clue for
Check Windows Authentication Advanced Settings -> enable kernel-mode is on and
Check check Enabled Providers like NTLM and Negotiate