Sync eng/common directory with azure-sdk-tools for PR 9202 (#31439)

Sync eng/common directory with azure-sdk-tools for PR
https://github.com/Azure/azure-sdk-tools/pull/9202 See [eng/common
workflow](https://github.com/Azure/azure-sdk-tools/blob/main/eng/common/README.md#workflow)

Co-authored-by: Ben Broderick Phillips <bebroder@microsoft.com>

eng/common/TestResources/New-TestResources.ps1

@@ -350,6 +350,10 @@ try {
         # to determine whether resources should be removed.
         Write-Host "Setting variable 'CI_HAS_DEPLOYED_RESOURCES': 'true'"
         LogVsoCommand "##vso[task.setvariable variable=CI_HAS_DEPLOYED_RESOURCES;]true"
+        # Set resource group env variable early in cases where deployment fails as we
+        # still want to clean up the group. The Remove-TestResources.ps1 script consumes this var.
+        $envVarName = (BuildServiceDirectoryPrefix $serviceName) + "RESOURCE_GROUP"
+        LogVsoCommand "##vso[task.setvariable variable=$envVarName;]$ResourceGroupName"
     }
 
     Log "Creating resource group '$ResourceGroupName' in location '$Location'"