Update AutoRest C# version to 3.0.0-beta.20250821.1 (Azure#52185)

* Update Generator Version 3.0.0-beta.20250821.1

* Update SDK codes mi_pu_4

* fix mysql

* fix postgresql

---------

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.20250820.2" PrivateAssets="All" />
+    <PackageReference Update="Microsoft.Azure.AutoRest.CSharp" Version="3.0.0-beta.20250821.1" 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.20250820.2"
+    "@azure-tools/typespec-csharp": "0.2.0-beta.20250821.1"
   },
   "devDependencies": {
     "@azure-tools/typespec-autorest": "0.59.0",

eng/emitter-package.json

@@ -0,0 +1,11 @@
+// Copyright (c) Microsoft Corporation. All rights reserved.
+// Licensed under the MIT License.
+
+using Azure.Core;
+
+namespace Azure.ResourceManager.MySql;
+
+[CodeGenType("AzureResourceManagerMySqlFlexibleServersContext")]
+public partial class AzureResourceManagerMySqlContext
+{
+}

sdk/mysql/Azure.ResourceManager.MySql/src/MySqlFlexibleServers/Custom/AzureResourceManagerMySqlContext.cs

@@ -0,0 +1,11 @@
+// Copyright (c) Microsoft Corporation. All rights reserved.
+// Licensed under the MIT License.
+
+using Azure.Core;
+
+namespace Azure.ResourceManager.PostgreSql;
+
+[CodeGenType("AzureResourceManagerPostgreSqlFlexibleServersContext")]
+public partial class AzureResourceManagerPostgreSqlContext
+{
+}