You're creating an array, not a scalar value. Arrays don't have a 'Version' property.
$InstallerName = "Install_Edge.ps1"
$Config_Content_Full = Import-Csv "c:\junk\Installer_versions.csv"
$Item = @($Config_Content_Full | Where-Object {$_.InstallerName -like $InstallerName})
$NotItem = @($Config_Content_Full | Where-Object {$_.InstallerName -notlike $InstallerName})
$Item |
ForEach-Object{
$_.Version
$_.Version = "AAAA"
}