[nightly] Update common Docker engineering infrastructure with latest (#6913)

Author: dotnet-docker-bot

eng/docker-tools/templates/jobs/cg-build-projects.yml

@@ -22,10 +22,10 @@ jobs:
     os: linux
   steps:
   - powershell: >
-      ./eng/docker-tools/Install-DotNetSdk.ps1 -Channel ${{ parameters.dotnetVersionChannel }} -InstallPath "$(Build.SourcesDirectory)/.dotnet"
+      ./eng/docker-tools/Install-DotNetSdk.ps1 -Channel ${{ parameters.dotnetVersionChannel }} -InstallPath "/usr/share/.dotnet"
     displayName: Run Dotnet Install Script
   - script: >
-      find . -name '*.csproj' | grep $(cgBuildGrepArgs) | xargs -n 1 $(Build.SourcesDirectory)/.dotnet/dotnet build
+      find . -name '*.csproj' | grep $(cgBuildGrepArgs) | xargs -n 1 /usr/share/.dotnet/dotnet build
     displayName: Build Projects
 
     # Component Detection is only automatically run on production branches.

eng/docker-tools/templates/jobs/copy-base-images-staging.yml

@@ -23,6 +23,7 @@ jobs:
   parameters:
     name: ${{ parameters.name }}
     pool: ${{ parameters.pool }}
+    publishConfig: ${{ parameters.publishConfig }}
     customInitSteps: ${{ parameters.customInitSteps }}
     additionalOptions: ${{ parameters.additionalOptions }}
     acr: ${{ parameters.publishConfig.InternalMirrorRegistry }}

eng/docker-tools/templates/jobs/copy-base-images.yml

@@ -5,6 +5,9 @@ parameters:
 - name: pool
   type: object
   default: {}
+- name: publishConfig
+  type: object
+  default: null
 - name: acr
   type: object
   default: null
@@ -26,6 +29,8 @@ jobs:
   pool: ${{ parameters.pool }}
   steps:
   - template: /eng/docker-tools/templates/steps/init-docker-linux.yml@self
+    parameters:
+      publishConfig: ${{ parameters.publishConfig }}
   - ${{ parameters.customInitSteps }}
   - template: /eng/docker-tools/templates/steps/copy-base-images.yml@self
     parameters:

eng/docker-tools/templates/stages/dotnet/publish-config-prod.yml

@@ -63,6 +63,7 @@ stages:
 
       PublicMirrorRegistry:
         server: $(public-mirror.server)
+        repoPrefix: $(mirrorRepoPrefix)
         resourceGroup: $(public-mirror.resourceGroup)
         subscription: $(public-mirror.subscription)
         serviceConnection: