[infra] Use PublicApiAnalyzers from NuGet.org (#6311)

Co-authored-by: Alan West <[email protected]>

Author: martincostello

NuGet.config

@@ -3,19 +3,14 @@
   <packageSources>
     <clear />
     <add key="NuGet" value="https://api.nuget.org/v3/index.json" />
-    <add key="dotnet8" value="https://dnceng.pkgs.visualstudio.com/public/_packaging/dotnet8/nuget/v3/index.json" />
   </packageSources>
 
   <!-- Define mappings by adding package patterns beneath the target source. -->
-  <!-- *.Tools packages will be restored from ".Net Core Tools", everything else from nuget.org. -->
   <packageSourceMapping>
     <!-- key value for <packageSource> should match key values from <packageSources> element -->
     <packageSource key="NuGet">
       <package pattern="*" />
     </packageSource>
-    <packageSource key="dotnet8">
-      <package pattern="Microsoft.CodeAnalysis.PublicApiAnalyzers" />
-    </packageSource>
   </packageSourceMapping>
 
   <disabledPackageSources />