Skip NuGet restores in PR Tools and authenticate publishing (#12297)

NuGet dependency updates can break PR previews when the Azure Artifacts
feed has not yet saved the requested versions from upstream, as seen in
#12296. PR Tools only
publishes the playground, website, and VS Code extension, so it does not
need to restore or build the .NET-based Visual Studio extension.

Skip that work in PR Tools and correct the .NET opt-in parameter so its
`false` default actually disables setup and restore. Publishing retains
its restores and now runs `NuGetAuthenticate@1` first; the E2E job
explicitly preserves its existing .NET setup.

Author: timotheeguerin

eng/tsp-core/pipelines/jobs/e2e.yml

@@ -21,6 +21,7 @@ jobs:
       - template: /eng/tsp-core/pipelines/templates/install.yml
         parameters:
           nodeVersion: 26.x
+          useDotNet: true
       - template: /eng/tsp-core/pipelines/templates/install-browsers.yml
       - template: /eng/tsp-core/pipelines/templates/setup-linux-ui.yml
       - template: /eng/tsp-core/pipelines/templates/build.yml

eng/tsp-core/pipelines/pr-tools.yml

@@ -28,6 +28,7 @@ extends:
             displayName: Setup Try It
             variables:
               TYPESPEC_WEBSITE_BASE_PATH: "/prs/$(System.PullRequest.PullRequestNumber)/"
+              TYPESPEC_SKIP_VS_BUILD: true
             steps:
               - checkout: self
                 persistCredentials: true

eng/tsp-core/pipelines/templates/install.yml

@@ -5,7 +5,7 @@ parameters:
     default: 24.16.0
 
   - name: useDotNet
-    type: string
+    type: boolean
     default: false
 
   - name: pnpmStorePath
@@ -37,6 +37,9 @@ steps:
     retryCountOnTaskFailure: 3
 
   - ${{ if parameters.useDotNet }}:
+      - task: NuGetAuthenticate@1
+        displayName: Authenticate NuGet feed
+
       - script: dotnet restore --configfile "$(Build.SourcesDirectory)/eng/nuget.config"
         displayName: Restore .NET Dependencies
         workingDirectory: packages/typespec-vs