Update Generator Version 3.0.0-beta.20251023.1 (#53475)

Author: azure-sdk

eng/Packages.Data.props

@@ -300,7 +300,7 @@
     All should have PrivateAssets="All" set so they don't become package dependencies
   -->
   <ItemGroup>
-    <PackageReference Update="Microsoft.Azure.AutoRest.CSharp" Version="3.0.0-beta.20251022.2" PrivateAssets="All" />
+    <PackageReference Update="Microsoft.Azure.AutoRest.CSharp" Version="3.0.0-beta.20251023.1" PrivateAssets="All" />
     <PackageReference Update="Azure.ClientSdk.Analyzers" Version="0.1.1-dev.20250715.1" PrivateAssets="All" />
     <PackageReference Update="coverlet.collector" Version="3.2.0" PrivateAssets="All" />
     <!-- Note: Upgrading the .NET SDK version needs to be synchronized with the autorest.csharp repository -->

eng/emitter-package-lock.json

@@ -1,7 +1,7 @@
 {
   "main": "dist/src/index.js",
   "dependencies": {
-    "@azure-tools/typespec-csharp": "0.2.0-beta.20251022.2"
+    "@azure-tools/typespec-csharp": "0.2.0-beta.20251023.1"
   },
   "devDependencies": {
     "@azure-tools/typespec-autorest": "0.61.0",