Update dependencies from https://github.com/dotnet/format build 20250612.1

dotnet-format
 From Version 8.1.617506 -> To Version 8.1.631201

Author: dotnet-maestro[bot]

NuGet.config

@@ -9,7 +9,7 @@
     <add key="darc-pub-dotnet-emsdk-2b0cca8-1" value="https://pkgs.dev.azure.com/dnceng/public/_packaging/darc-pub-dotnet-emsdk-2b0cca8a-1/nuget/v3/index.json" />
     <!--  End: Package sources from dotnet-emsdk -->
     <!--  Begin: Package sources from dotnet-format -->
-    <add key="darc-pub-dotnet-format-664013f" value="https://pkgs.dev.azure.com/dnceng/public/_packaging/darc-pub-dotnet-format-664013fb/nuget/v3/index.json" />
+    <add key="darc-pub-dotnet-format-7332bce" value="https://pkgs.dev.azure.com/dnceng/public/_packaging/darc-pub-dotnet-format-7332bce1/nuget/v3/index.json" />
     <!--  End: Package sources from dotnet-format -->
     <!--  Begin: Package sources from dotnet-aspnetcore -->
     <add key="darc-int-dotnet-aspnetcore-fa4d80b" value="https://pkgs.dev.azure.com/dnceng/internal/_packaging/darc-int-dotnet-aspnetcore-fa4d80b7/nuget/v3/index.json" />
@@ -30,7 +30,6 @@
     <!--  End: Package sources from dotnet-runtime -->
     <!--  Begin: Package sources from dotnet-templating -->
     <add key="darc-pub-dotnet-templating-2a22f25" value="https://pkgs.dev.azure.com/dnceng/public/_packaging/darc-pub-dotnet-templating-2a22f253/nuget/v3/index.json" />
-    <add key="darc-pub-dotnet-templating-f03f218" value="https://pkgs.dev.azure.com/dnceng/public/_packaging/darc-pub-dotnet-templating-f03f218a/nuget/v3/index.json" />
     <!--  End: Package sources from dotnet-templating -->
     <!--  Begin: Package sources from dotnet-windowsdesktop -->
     <add key="darc-int-dotnet-windowsdesktop-5ce68f2" value="https://pkgs.dev.azure.com/dnceng/internal/_packaging/darc-int-dotnet-windowsdesktop-5ce68f29/nuget/v3/index.json" />

eng/Version.Details.xml

@@ -77,9 +77,9 @@
       <Sha>fc5e9eda234e2b69aa479f4f83faddc31fdd4da7</Sha>
       <SourceBuild RepoName="fsharp" ManagedOnly="true" />
     </Dependency>
-    <Dependency Name="dotnet-format" Version="8.1.617506">
+    <Dependency Name="dotnet-format" Version="8.1.631201">
       <Uri>https://github.com/dotnet/format</Uri>
-      <Sha>664013fbe5e68941be81f9a710058db028da788f</Sha>
+      <Sha>7332bce179c114a5490773119053f561faf58a33</Sha>
       <SourceBuild RepoName="format" ManagedOnly="true" />
     </Dependency>
     <Dependency Name="Microsoft.Net.Compilers.Toolset" Version="4.8.0-7.25056.18">

eng/Versions.props

@@ -112,7 +112,7 @@
   </PropertyGroup>
   <PropertyGroup>
     <!-- Dependencies from https://github.com/dotnet/format -->
-    <dotnetformatVersion>8.1.617506</dotnetformatVersion>
+    <dotnetformatVersion>8.1.631201</dotnetformatVersion>
   </PropertyGroup>
   <PropertyGroup>
     <!-- Dependencies from https://github.com/dotnet/roslyn-analyzers -->