Update dependencies from https://github.com/dotnet/roslyn-analyzers build 20241027.2

Microsoft.SourceBuild.Intermediate.roslyn-analyzers , Microsoft.CodeAnalysis.NetAnalyzers , Microsoft.CodeAnalysis.PublicApiAnalyzers
 From Version 3.11.0-beta1.24508.2 -> To Version 3.11.0-beta1.24527.2

Author: dotnet-maestro[bot]

NuGet.config

@@ -4,8 +4,6 @@
     <clear />
     <!--Begin: Package sources managed by Dependency Flow automation. Do not edit the sources below.-->
     <!--  Begin: Package sources from dotnet-aspire -->
-    <add key="darc-pub-dotnet-aspire-5fa9337" value="https://pkgs.dev.azure.com/dnceng/public/_packaging/darc-pub-dotnet-aspire-5fa9337a/nuget/v3/index.json" />
-    <add key="darc-pub-dotnet-aspire-5fa9337-1" value="https://pkgs.dev.azure.com/dnceng/public/_packaging/darc-pub-dotnet-aspire-5fa9337a-1/nuget/v3/index.json" />
     <!--  End: Package sources from dotnet-aspire -->
     <!--  Begin: Package sources from dotnet-emsdk -->
     <add key="darc-pub-dotnet-emsdk-8be5676" value="https://pkgs.dev.azure.com/dnceng/public/_packaging/darc-pub-dotnet-emsdk-8be5676a/nuget/v3/index.json" />
@@ -23,6 +21,9 @@
     <!--  End: Package sources from dotnet-runtime -->
     <!--  Begin: Package sources from dotnet-templating -->
     <add key="darc-pub-dotnet-templating-e07a90b" value="https://pkgs.dev.azure.com/dnceng/public/_packaging/darc-pub-dotnet-templating-e07a90b4/nuget/v3/index.json" />
+    <add key="darc-pub-dotnet-templating-e07a90b-5" value="https://pkgs.dev.azure.com/dnceng/public/_packaging/darc-pub-dotnet-templating-e07a90b4-5/nuget/v3/index.json" />
+    <add key="darc-pub-dotnet-templating-e07a90b-4" value="https://pkgs.dev.azure.com/dnceng/public/_packaging/darc-pub-dotnet-templating-e07a90b4-4/nuget/v3/index.json" />
+    <add key="darc-pub-dotnet-templating-e07a90b-3" value="https://pkgs.dev.azure.com/dnceng/public/_packaging/darc-pub-dotnet-templating-e07a90b4-3/nuget/v3/index.json" />
     <add key="darc-pub-dotnet-templating-e07a90b-2" value="https://pkgs.dev.azure.com/dnceng/public/_packaging/darc-pub-dotnet-templating-e07a90b4-2/nuget/v3/index.json" />
     <add key="darc-pub-dotnet-templating-e07a90b-1" value="https://pkgs.dev.azure.com/dnceng/public/_packaging/darc-pub-dotnet-templating-e07a90b4-1/nuget/v3/index.json" />
     <!--  End: Package sources from dotnet-templating -->

eng/Version.Details.xml

@@ -408,16 +408,16 @@
       <Sha>1a54480f52703fb45fac2a6b955247d33758383e</Sha>
       <SourceBuild RepoName="xdt" ManagedOnly="true" />
     </Dependency>
-    <Dependency Name="Microsoft.CodeAnalysis.NetAnalyzers" Version="9.0.0-preview.24508.2">
+    <Dependency Name="Microsoft.CodeAnalysis.NetAnalyzers" Version="9.0.0-preview.24527.2">
       <Uri>https://github.com/dotnet/roslyn-analyzers</Uri>
       <Sha>3d61c57c73c3dd5f1f407ef9cd3414d94bf0eaf2</Sha>
     </Dependency>
-    <Dependency Name="Microsoft.CodeAnalysis.PublicApiAnalyzers" Version="3.11.0-beta1.24508.2">
+    <Dependency Name="Microsoft.CodeAnalysis.PublicApiAnalyzers" Version="3.11.0-beta1.24527.2">
       <Uri>https://github.com/dotnet/roslyn-analyzers</Uri>
       <Sha>3d61c57c73c3dd5f1f407ef9cd3414d94bf0eaf2</Sha>
     </Dependency>
     <!-- Intermediate is necessary for source build. -->
-    <Dependency Name="Microsoft.SourceBuild.Intermediate.roslyn-analyzers" Version="3.11.0-beta1.24508.2">
+    <Dependency Name="Microsoft.SourceBuild.Intermediate.roslyn-analyzers" Version="3.11.0-beta1.24527.2">
       <Uri>https://github.com/dotnet/roslyn-analyzers</Uri>
       <Sha>3d61c57c73c3dd5f1f407ef9cd3414d94bf0eaf2</Sha>
       <SourceBuild RepoName="roslyn-analyzers" ManagedOnly="true" />

eng/Versions.props

@@ -174,8 +174,8 @@
   </PropertyGroup>
   <PropertyGroup>
     <!-- Dependencies from https://github.com/dotnet/roslyn-analyzers -->
-    <MicrosoftCodeAnalysisNetAnalyzersVersion>9.0.0-preview.24508.2</MicrosoftCodeAnalysisNetAnalyzersVersion>
-    <MicrosoftCodeAnalysisPublicApiAnalyzersVersion>3.11.0-beta1.24508.2</MicrosoftCodeAnalysisPublicApiAnalyzersVersion>
+    <MicrosoftCodeAnalysisNetAnalyzersVersion>9.0.0-preview.24527.2</MicrosoftCodeAnalysisNetAnalyzersVersion>
+    <MicrosoftCodeAnalysisPublicApiAnalyzersVersion>3.11.0-beta1.24527.2</MicrosoftCodeAnalysisPublicApiAnalyzersVersion>
   </PropertyGroup>
   <PropertyGroup>
     <!-- Dependencies from https://github.com/Microsoft/msbuild -->