[release/8.0-staging] Update dependencies from dotnet/icu (#121675)

This pull request updates the following dependencies

[marker]: <> (Begin:e82a8e07-8d2b-4a71-e90f-08dbcfd41ade)
## From https://github.com/dotnet/icu
- **Subscription**:
[e82a8e07-8d2b-4a71-e90f-08dbcfd41ade](https://maestro.dot.net/subscriptions?search=e82a8e07-8d2b-4a71-e90f-08dbcfd41ade)
- **Build**:
[20251115.1](https://dev.azure.com/dnceng/internal/_build/results?buildId=2839873)
([291019](https://maestro.dot.net/channel/3073/github:dotnet:icu/build/291019))
- **Date Produced**: November 15, 2025 5:11:34 PM UTC
- **Commit**:
[b565264ebc86c4444a7a5d411f69674393d61265](dotnet/icu@b565264)
- **Branch**:
[dotnet/release/8.0](https://github.com/dotnet/icu/tree/dotnet/release/8.0)

[DependencyUpdate]: <> (Begin)

- **Dependency Updates**:
  - From [8.0.0-rtm.25522.4 to 8.0.0-rtm.25565.1][1]
     - Microsoft.NETCore.Runtime.ICU.Transport

[1]: dotnet/icu@889994e...b565264

[DependencyUpdate]: <> (End)


[marker]: <> (End:e82a8e07-8d2b-4a71-e90f-08dbcfd41ade)

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

Author: dotnet-maestro[bot]

NuGet.config

@@ -9,6 +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-9e37ff5" value="https://pkgs.dev.azure.com/dnceng/public/_packaging/darc-pub-dotnet-emsdk-9e37ff5e/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

@@ -1,8 +1,8 @@
 <Dependencies>
   <ProductDependencies>
-    <Dependency Name="Microsoft.NETCore.Runtime.ICU.Transport" Version="8.0.0-rtm.25522.4">
+    <Dependency Name="Microsoft.NETCore.Runtime.ICU.Transport" Version="8.0.0-rtm.25565.1">
       <Uri>https://github.com/dotnet/icu</Uri>
-      <Sha>889994ebb9fa2ba6183182bba33b260c645a8089</Sha>
+      <Sha>b565264ebc86c4444a7a5d411f69674393d61265</Sha>
     </Dependency>
     <Dependency Name="System.Net.MsQuic.Transport" Version="8.0.0-alpha.1.23527.1">
       <Uri>https://github.com/dotnet/msquic</Uri>

eng/Versions.props

@@ -229,7 +229,7 @@
     <!-- ILCompiler -->
     <MicrosoftDotNetILCompilerVersion>8.0.0-rc.1.23406.6</MicrosoftDotNetILCompilerVersion>
     <!-- ICU -->
-    <MicrosoftNETCoreRuntimeICUTransportVersion>8.0.0-rtm.25522.4</MicrosoftNETCoreRuntimeICUTransportVersion>
+    <MicrosoftNETCoreRuntimeICUTransportVersion>8.0.0-rtm.25565.1</MicrosoftNETCoreRuntimeICUTransportVersion>
     <!-- MsQuic -->
     <MicrosoftNativeQuicMsQuicSchannelVersion>2.4.8</MicrosoftNativeQuicMsQuicSchannelVersion>
     <!-- Mono LLVM -->