Update AutoRest C# version to 3.0.0-beta.20250821.2 (Azure#52186)

* Update Generator Version 3.0.0-beta.20250821.2

* Update SDK codes co_da_1

* export api

---------

Co-authored-by: Arcturus Zhang <[email protected]>

Author: azure-sdk

eng/Packages.Data.props

@@ -293,7 +293,7 @@
     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.20250821.1" PrivateAssets="All" />
+    <PackageReference Update="Microsoft.Azure.AutoRest.CSharp" Version="3.0.0-beta.20250821.2" 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

@@ -1,14 +1,14 @@
 {
   "main": "dist/src/index.js",
   "dependencies": {
-    "@azure-tools/typespec-csharp": "0.2.0-beta.20250821.1"
+    "@azure-tools/typespec-csharp": "0.2.0-beta.20250821.2"
   },
   "devDependencies": {
     "@azure-tools/typespec-autorest": "0.59.0",
     "@azure-tools/typespec-azure-core": "0.59.0",
-    "@azure-tools/typespec-azure-resource-manager": "0.59.0",
+    "@azure-tools/typespec-azure-resource-manager": "0.59.2",
     "@azure-tools/typespec-azure-rulesets": "0.59.0",
-    "@azure-tools/typespec-client-generator-core": "0.59.0",
+    "@azure-tools/typespec-client-generator-core": "0.59.1",
     "@azure-tools/typespec-liftr-base": "0.8.0",
     "@typespec/compiler": "1.3.0",
     "@typespec/events": "0.73.0",