[release/9.0] Update dependencies from dotnet/emsdk (#120814)

This pull request updates the following dependencies

[marker]: <> (Begin:f85f62c8-5e7d-4706-1003-08dcbc30275f)
## From https://github.com/dotnet/emsdk
- **Subscription**:
[f85f62c8-5e7d-4706-1003-08dcbc30275f](https://maestro.dot.net/subscriptions?search=f85f62c8-5e7d-4706-1003-08dcbc30275f)
- **Build**:
[20251016.4](https://dev.azure.com/dnceng/internal/_build/results?buildId=2817718)
([287477](https://maestro.dot.net/channel/3883/github:dotnet:emsdk/build/287477))
- **Date Produced**: October 16, 2025 5:47:56 PM UTC
- **Commit**:
[b65413ac057eb0a54c51b76b1855bc377c2132c3](dotnet/emsdk@b65413a)
- **Branch**:
[release/9.0](https://github.com/dotnet/emsdk/tree/release/9.0)

[DependencyUpdate]: <> (Begin)

- **Updates**:
  - From [9.0.11-servicing.25515.5 to 9.0.11-servicing.25516.4][1]
     - Microsoft.SourceBuild.Intermediate.emsdk
- Microsoft.NET.Workload.Emscripten.Current.Manifest-9.0.100.Transport
  - From [9.0.11 to 9.0.11][1]
     - Microsoft.NET.Workload.Emscripten.Current.Manifest-9.0.100

[1]: dotnet/emsdk@13de364...b65413a

[DependencyUpdate]: <> (End)


[marker]: <> (End:f85f62c8-5e7d-4706-1003-08dcbc30275f)

Co-authored-by: dotnet-maestro[bot] <dotnet-maestro[bot]@users.noreply.github.com>

Author: dotnet-maestro[bot]

NuGet.config

@@ -9,7 +9,7 @@
     <clear />
     <!--Begin: Package sources managed by Dependency Flow automation. Do not edit the sources below.-->
     <!--  Begin: Package sources from dotnet-emsdk -->
-    <add key="darc-pub-dotnet-emsdk-13de364" value="https://pkgs.dev.azure.com/dnceng/public/_packaging/darc-pub-dotnet-emsdk-13de3640/nuget/v3/index.json" />
+    <add key="darc-pub-dotnet-emsdk-b65413a" value="https://pkgs.dev.azure.com/dnceng/public/_packaging/darc-pub-dotnet-emsdk-b65413ac/nuget/v3/index.json" />
     <!--  End: Package sources from dotnet-emsdk -->
     <!--  Begin: Package sources from dotnet-sdk -->
     <!--  End: Package sources from dotnet-sdk -->

eng/Version.Details.xml

@@ -64,18 +64,18 @@
       <Sha>1b55accc7029bd4038d35b2072ec58841431122f</Sha>
       <SourceBuild RepoName="cecil" ManagedOnly="true" />
     </Dependency>
-    <Dependency Name="Microsoft.NET.Workload.Emscripten.Current.Manifest-9.0.100.Transport" Version="9.0.11-servicing.25515.5">
+    <Dependency Name="Microsoft.NET.Workload.Emscripten.Current.Manifest-9.0.100.Transport" Version="9.0.11-servicing.25516.4">
       <Uri>https://github.com/dotnet/emsdk</Uri>
-      <Sha>13de3640b5fdb3a2b9ec46bba632a72fd74c449c</Sha>
+      <Sha>b65413ac057eb0a54c51b76b1855bc377c2132c3</Sha>
     </Dependency>
     <Dependency Name="Microsoft.NET.Workload.Emscripten.Current.Manifest-9.0.100" Version="9.0.11">
       <Uri>https://github.com/dotnet/emsdk</Uri>
-      <Sha>13de3640b5fdb3a2b9ec46bba632a72fd74c449c</Sha>
+      <Sha>b65413ac057eb0a54c51b76b1855bc377c2132c3</Sha>
     </Dependency>
     <!-- Intermediate is necessary for source build. -->
-    <Dependency Name="Microsoft.SourceBuild.Intermediate.emsdk" Version="9.0.11-servicing.25515.5">
+    <Dependency Name="Microsoft.SourceBuild.Intermediate.emsdk" Version="9.0.11-servicing.25516.4">
       <Uri>https://github.com/dotnet/emsdk</Uri>
-      <Sha>13de3640b5fdb3a2b9ec46bba632a72fd74c449c</Sha>
+      <Sha>b65413ac057eb0a54c51b76b1855bc377c2132c3</Sha>
       <SourceBuild RepoName="emsdk" ManagedOnly="true" />
     </Dependency>
     <!-- Intermediate is necessary for source build. -->

eng/Versions.props

@@ -250,7 +250,7 @@
          Note: when the name is updated, make sure to update dependency name in eng/pipelines/common/xplat-setup.yml
                like - DarcDependenciesChanged.Microsoft_NET_Workload_Emscripten_Current_Manifest-9_0_100_Transport
     -->
-    <MicrosoftNETWorkloadEmscriptenCurrentManifest90100TransportVersion>9.0.11-servicing.25515.5</MicrosoftNETWorkloadEmscriptenCurrentManifest90100TransportVersion>
+    <MicrosoftNETWorkloadEmscriptenCurrentManifest90100TransportVersion>9.0.11-servicing.25516.4</MicrosoftNETWorkloadEmscriptenCurrentManifest90100TransportVersion>
     <MicrosoftNETWorkloadEmscriptenCurrentManifest90100Version>9.0.11</MicrosoftNETWorkloadEmscriptenCurrentManifest90100Version>
     <MicrosoftNETRuntimeEmscriptenVersion>$(MicrosoftNETWorkloadEmscriptenCurrentManifest90100Version)</MicrosoftNETRuntimeEmscriptenVersion>
     <!-- workloads -->