Why Error "System.String does not contain a method named 'AppendChild'" - powershell

Question

Why does this PowerShell Script not work:
[xml]$xml = '<products></products>'
$newproduct = $xml.CreateElement('product')
$attr = $xml.CreateAttribute('code')
$attr.Value = 'id1'
$newproduct.Attributes.Append($attr)
$products = $xml.products
$products.AppendChild($newproduct)
Error is
Method invocation failed because [System.String] does not contain a method named 'AppendChild'.
At line:1 char:1
+ $products.AppendChild($newproduct)
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+ CategoryInfo : InvalidOperation: (:) [], RuntimeException
+ FullyQualifiedErrorId : MethodNotFound
If I replace
$products = $xml.products
by
$products = $xml.SelectSingleNode('//products')
it will work, but I'd like to know why first syntax does not work because it is illogical for me. $xml.products should be a valid XML object and thus provide the method AppendChild().

Answer 1

$xml.products does not reference the products node itself, but the contents of the products node. Since products is empty, it evaluates to an empty string.
To get to the products node you could also use:
$Products = $xml.FirstChild
$Products.AppendChild($newproduct)
or, more specifically:
$Products = $xml.ChildNodes.Where({$_.Name -eq "products"}) |Select-Object -First 1
$Products.AppendChild($newproduct)
But SelectSingleNode() will probably serve you just fine

Answer 2

$xml.configuration.SelectSingleNode("connectionStrings").AppendChild($newnode)
would work fine, but an interesting & dirty hack: given this empty node:
<connectionStrings>
</connectionStrings>
the script
$xml.configuration.connectionStrings.AppendChild($newnode)
gives a "Method invocation failed because [System.String] does not contain a method named 'AppendChild'" error
but this:
<connectionStrings>
<!-- random comment -->
</connectionStrings>
works perfectly fine