Sync eng/common directory with azure-sdk-tools for PR 2249 (#25264)

* notify of running build

* get rid of extraneous path setting

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

Author: azure-sdk

eng/common/testproxy/test-proxy-docker.yml

@@ -16,4 +16,8 @@ steps:
 
   - pwsh: |
       docker container ls -a
-    displayName: Check running container
+    displayName: Check running container
+
+  - pwsh: |
+      Write-Host "##vso[task.setvariable variable=PROXY_MANUAL_START]true"
+    displayName: 'Set PROXY_MANUAL_START'

eng/common/testproxy/test-proxy-tool.yml

@@ -6,14 +6,11 @@ steps:
         $(Build.SourcesDirectory)/eng/common/scripts/trust-proxy-certificate.ps1
     displayName: 'Language Specific Certificate Trust'
 
-  - pwsh: |
-      Write-Host "##vso[task.setvariable variable=OriginalPath]$env:PATH"
-    displayName: 'Store Path Value'
-
   - pwsh: |
       Write-Host "##vso[task.setvariable variable=ASPNETCORE_Kestrel__Certificates__Default__Path]$(Build.SourcesDirectory)/eng/common/testproxy/dotnet-devcert.pfx"
       Write-Host "##vso[task.setvariable variable=ASPNETCORE_Kestrel__Certificates__Default__Password]password"
-    displayName: 'Configure Kestrel Environment Variables'
+      Write-Host "##vso[task.setvariable variable=PROXY_MANUAL_START]true"
+    displayName: 'Configure Kestrel and PROXY_MANUAL_START Variables'
 
   - pwsh: |
       dotnet tool install azure.sdk.tools.testproxy `