[main] Update common Docker engineering infrastructure with latest (#4790)

eng/common/templates/stages/dotnet/build-test-publish-repo.yml

@@ -82,10 +82,4 @@ stages:
         name: Docker-Linux-Arm-Internal
     windows2016Pool: Docker-2016-${{ variables['System.TeamProject'] }}
     windows1809Pool: Docker-1809-${{ variables['System.TeamProject'] }}
-    windows2022Pool:
-      ${{ if eq(variables['System.TeamProject'], parameters.publicProjectName) }}:
-        name: NetCore-Public
-        demands: ImageOverride -equals 1es-windows-2022-open
-      ${{ if eq(variables['System.TeamProject'], parameters.internalProjectName) }}:
-        name: NetCore1ESPool-Svc-Internal
-        demands: ImageOverride -equals 1es-windows-2022
+    windows2022Pool: Docker-2022-${{ variables['System.TeamProject'] }}

eng/common/templates/variables/docker-images.yml

@@ -1,5 +1,5 @@
 variables:
-  imageNames.imageBuilderName: mcr.microsoft.com/dotnet-buildtools/image-builder:2230260
+  imageNames.imageBuilderName: mcr.microsoft.com/dotnet-buildtools/image-builder:2233114
   imageNames.imageBuilder: $(imageNames.imageBuilderName)
   imageNames.imageBuilder.withrepo: imagebuilder-withrepo:$(Build.BuildId)-$(System.JobId)
   imageNames.testRunner: mcr.microsoft.com/dotnet-buildtools/prereqs:debian-bullseye-slim-docker-testrunner