Update AutoRest C# version to 3.0.0-beta.20250113.1 (Azure#47824)

* Update Generator Version 3.0.0-beta.20250113.1

* Update SDK codes pu_sp_5

Author: azure-sdk

eng/Packages.Data.props

@@ -243,7 +243,7 @@
     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.20250109.1" PrivateAssets="All" />
+    <PackageReference Update="Microsoft.Azure.AutoRest.CSharp" Version="3.0.0-beta.20250113.1" PrivateAssets="All" />
     <PackageReference Update="Azure.ClientSdk.Analyzers" Version="0.1.1-dev.20240813.2" PrivateAssets="All" />
     <PackageReference Update="coverlet.collector" Version="3.2.0" PrivateAssets="All" />
     <PackageReference Update="Microsoft.CodeAnalysis.NetAnalyzers" Version="8.0.0" PrivateAssets="All" />

eng/emitter-package-lock.json

@@ -1,14 +1,15 @@
 {
   "main": "dist/src/index.js",
   "dependencies": {
-    "@azure-tools/typespec-csharp": "0.2.0-beta.20250109.1"
+    "@azure-tools/typespec-csharp": "0.2.0-beta.20250113.1"
   },
   "devDependencies": {
     "@azure-tools/typespec-autorest": "0.49.0",
     "@azure-tools/typespec-azure-core": "0.49.0",
     "@azure-tools/typespec-azure-resource-manager": "0.49.0",
     "@azure-tools/typespec-azure-rulesets": "0.49.0",
     "@azure-tools/typespec-client-generator-core": "0.49.1",
+    "@azure-tools/typespec-liftr-base": "0.6.0",
     "@typespec/compiler": "0.63.0",
     "@typespec/http": "0.63.0",
     "@typespec/openapi": "0.63.0",