Update dependencies from https://github.com/dotnet/templating build 20241029.1

Microsoft.SourceBuild.Intermediate.templating , Microsoft.TemplateEngine.Abstractions , Microsoft.TemplateEngine.Mocks
 From Version 10.0.100-alpha.1.24527.1 -> To Version 10.0.100-alpha.1.24529.1

Author: dotnet-maestro[bot]

eng/Version.Details.xml

@@ -1,18 +1,18 @@
 <?xml version="1.0" encoding="utf-8"?>
 <Dependencies>
   <ProductDependencies>
-    <Dependency Name="Microsoft.TemplateEngine.Abstractions" Version="10.0.100-alpha.1.24528.2">
+    <Dependency Name="Microsoft.TemplateEngine.Abstractions" Version="10.0.100-alpha.1.24529.1">
       <Uri>https://github.com/dotnet/templating</Uri>
-      <Sha>7f9456830c8fc7c69d6b7c101aeecc6672f8cb5d</Sha>
+      <Sha>9b4a701787b1a51ebfdc5cf222ea8511f58b5411</Sha>
     </Dependency>
-    <Dependency Name="Microsoft.TemplateEngine.Mocks" Version="10.0.100-alpha.1.24528.2">
+    <Dependency Name="Microsoft.TemplateEngine.Mocks" Version="10.0.100-alpha.1.24529.1">
       <Uri>https://github.com/dotnet/templating</Uri>
-      <Sha>7f9456830c8fc7c69d6b7c101aeecc6672f8cb5d</Sha>
+      <Sha>9b4a701787b1a51ebfdc5cf222ea8511f58b5411</Sha>
     </Dependency>
     <!-- Intermediate is necessary for source build. -->
-    <Dependency Name="Microsoft.SourceBuild.Intermediate.templating" Version="10.0.100-alpha.1.24528.2">
+    <Dependency Name="Microsoft.SourceBuild.Intermediate.templating" Version="10.0.100-alpha.1.24529.1">
       <Uri>https://github.com/dotnet/templating</Uri>
-      <Sha>7f9456830c8fc7c69d6b7c101aeecc6672f8cb5d</Sha>
+      <Sha>9b4a701787b1a51ebfdc5cf222ea8511f58b5411</Sha>
       <SourceBuild RepoName="templating" ManagedOnly="true" />
     </Dependency>
     <Dependency Name="Microsoft.NETCore.App.Ref" Version="10.0.0-alpha.1.24528.7">

eng/Versions.props

@@ -226,13 +226,13 @@
   </PropertyGroup>
   <PropertyGroup>
     <!-- Dependencies from https://github.com/dotnet/templating -->
-    <MicrosoftTemplateEngineAbstractionsPackageVersion>10.0.100-alpha.1.24528.2</MicrosoftTemplateEngineAbstractionsPackageVersion>
+    <MicrosoftTemplateEngineAbstractionsPackageVersion>10.0.100-alpha.1.24529.1</MicrosoftTemplateEngineAbstractionsPackageVersion>
     <MicrosoftTemplateEngineEdgePackageVersion>$(MicrosoftTemplateEngineAbstractionsPackageVersion)</MicrosoftTemplateEngineEdgePackageVersion>
     <MicrosoftTemplateEngineOrchestratorRunnableProjectsPackageVersion>$(MicrosoftTemplateEngineAbstractionsPackageVersion)</MicrosoftTemplateEngineOrchestratorRunnableProjectsPackageVersion>
     <MicrosoftTemplateEngineUtilsPackageVersion>$(MicrosoftTemplateEngineAbstractionsPackageVersion)</MicrosoftTemplateEngineUtilsPackageVersion>
     <MicrosoftTemplateSearchCommonPackageVersion>$(MicrosoftTemplateEngineAbstractionsPackageVersion)</MicrosoftTemplateSearchCommonPackageVersion>
     <!-- test dependencies -->
-    <MicrosoftTemplateEngineMocksPackageVersion>10.0.100-alpha.1.24528.2</MicrosoftTemplateEngineMocksPackageVersion>
+    <MicrosoftTemplateEngineMocksPackageVersion>10.0.100-alpha.1.24529.1</MicrosoftTemplateEngineMocksPackageVersion>
     <MicrosoftTemplateEngineTestHelperPackageVersion>$(MicrosoftTemplateEngineMocksPackageVersion)</MicrosoftTemplateEngineTestHelperPackageVersion>
     <MicrosoftTemplateEngineAuthoringTemplateVerifierVersion>$(MicrosoftTemplateEngineAbstractionsPackageVersion)</MicrosoftTemplateEngineAuthoringTemplateVerifierVersion>
     <MicrosoftTemplateSearchTemplateDiscoveryPackageVersion>$(MicrosoftTemplateEngineMocksPackageVersion)</MicrosoftTemplateSearchTemplateDiscoveryPackageVersion>