Update script to support running on GH action (Azure#50616)

Co-authored-by: Praveen Kuttappan <[email protected]>

Author: azure-sdk

eng/common/mcp/azure-sdk-mcp.ps1

@@ -4,7 +4,7 @@ param(
     [string]$FileName = 'Azure.Sdk.Tools.Cli',
     [string]$Package = 'azsdk',
     [string]$Version, # Default to latest
-    [string]$InstallDirectory = (Join-Path $HOME ".azure-sdk-mcp" "azsdk"),
+    [string]$InstallDirectory = '',
     [string]$Repository = 'Azure/azure-sdk-tools',
     [string]$RunDirectory = (Resolve-Path (Join-Path $PSScriptRoot .. .. ..)),
     [switch]$Run,
@@ -14,6 +14,11 @@ param(
 
 $ErrorActionPreference = "Stop"
 
+if (-not $InstallDirectory)
+{
+    $homeDir = if ($env:HOME) { $env:HOME } else { $env:USERPROFILE }
+    $InstallDirectory = (Join-Path $homeDir ".azure-sdk-mcp" "azsdk")
+}
 . (Join-Path $PSScriptRoot '..' 'scripts' 'Helpers' 'AzSdkTool-Helpers.ps1')
 
 if ($Clean) {