Grouping and totaling a sub-element of repeating elements in XML

A Group-Object solution that modifies the XML document in place:

# Parse the XML file into a DOM.
# Replace "sample.xml" with your XML file path.
($xmlDoc = [xml]::new()).Load((Convert-Path sample.xml))

# Loop over all <Item> elements.
$xmlDoc.Inventory.Item | 
  Group-Object ItemType, ItemId, Color | 
  Where-Object Count -gt 1 | 
  ForEach-Object {
    # Sum up all MinQty values and assign the sum to the first element
    # in the group.
    $_.Group[0].MinQty = [string] ($_.Group.MinQty | Measure-Object -Sum).Sum
    # Now remove all other elements in the group.
    $null = $_.Group[1..($_.Count-1)].ForEach({ $_.ParentNode.RemoveChild($_) })
  }

Note:

• Casting the .Sum value to [string] explicitly is only required in Windows PowerShell, where only an actual string ([string] instance) is accepted on assignment to an XML element.
  PowerShell (Core) 7+, more conveniently performs stringification on demand.

• A simple example:

   # OK in PS 7+: integer 2 is automatically converted to string.
   # In WinPS, you get the following error:
   #   Cannot set "el" because only strings can be used as 
   #   values to set XmlNode properties.'
   ($x = [xml] '<el>1</el>').el = 2 
  
   # Required in Windows PowerShell: RHS must be an actual string.
   ($x = [xml] '<el>1</el>').el = [string] 2 # simple alternative here: '2' 
  

Printing the XML text of the updated DOM, as shown below, matches the expected result in your question:

if ($IsCoreCLR) { # PowerShell (Core) 7+
  # Pretty-print
  ([System.Xml.Linq.XDocument] $xmlDoc.OuterXml).ToString()
} else { # Windows PowerShell 
  # No pretty-printing easily available, just print .OuterXml
  $xmlDoc.OuterXml
}