Sync eng/common directory with azure-sdk-tools for PR 10969 (#6639)

* Fix vscode config auto-install in mcp script

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

Co-authored-by: Scott Beddall <45376673+scbedd@users.noreply.github.com>

---------

Co-authored-by: Ben Broderick Phillips <bebroder@microsoft.com>
Co-authored-by: Scott Beddall <45376673+scbedd@users.noreply.github.com>

Author: 3 people

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

@@ -26,17 +26,17 @@ if ($Clean) {
 }
 
 if ($UpdateVsCodeConfig) {
-    $vscodeConfigPath = $PSScriptRoot + "../../../.vscode/mcp.json"
+    $vscodeConfigPath = Join-Path $PSScriptRoot ".." ".." ".." ".vscode" "mcp.json"
     if (Test-Path $vscodeConfigPath) {
-        $vscodeConfig = Get-Content -Raw $vscodeConfig | ConvertFrom-Json -AsHashtable
+        $vscodeConfig = Get-Content -Raw $vscodeConfigPath | ConvertFrom-Json -AsHashtable
     }
     else {
         $vscodeConfig = @{}
     }
     $serverKey = "azure-sdk-mcp"
     $serverConfig = @{
         "type"    = "stdio"
-        "command" = "/home/ben/azs/azure-sdk-tools/eng/common/mcp/azure-sdk-mcp.ps1"
+        "command" = "$PSCommandPath"
     }
     $orderedServers = [ordered]@{
         $serverKey = $serverConfig