Update dependencies from https://github.com/dotnet/arcade build 20251007.1

On relative base path root
Microsoft.DotNet.Arcade.Sdk From Version 10.0.0-beta.25476.2 -> To Version 10.0.0-beta.25507.1

Author: dotnet-maestro[bot]

eng/Version.Details.xml

@@ -40,9 +40,9 @@
     </Dependency>
   </ProductDependencies>
   <ToolsetDependencies>
-    <Dependency Name="Microsoft.DotNet.Arcade.Sdk" Version="10.0.0-beta.25479.4">
+    <Dependency Name="Microsoft.DotNet.Arcade.Sdk" Version="10.0.0-beta.25507.1">
       <Uri>https://github.com/dotnet/arcade</Uri>
-      <Sha>e6f510cb87812d56ad781d93ff0513cdcccd0eb4</Sha>
+      <Sha>4eaa220ea860cee9fa61df42411bbf79394edd23</Sha>
       <SourceBuild RepoName="arcade" ManagedOnly="true" />
     </Dependency>
   </ToolsetDependencies>

global.json

@@ -9,7 +9,7 @@
   },
   "msbuild-sdks": {
     "Microsoft.Build.NoTargets": "3.7.0",
-    "Microsoft.DotNet.Arcade.Sdk": "10.0.0-beta.25479.4",
+    "Microsoft.DotNet.Arcade.Sdk": "10.0.0-beta.25507.1",
     "Microsoft.VisualStudio.Internal.MicroBuild.Vsman": "2.0.174"
   }
 }