[docs] Obsolete PublishAsConnectionString migration guidance

src/frontend/src/content/docs/fundamentals/external-parameters.mdx

@@ -619,9 +619,11 @@ To express a parameter, consider the following example code:
 ```csharp title="AppHost.cs"
 var builder = DistributedApplication.CreateBuilder(args);
 
-var db = builder.AddSqlServer("sql")
-                .PublishAsConnectionString()
-                .AddDatabase("db");
+// In run mode, add the actual SQL Server resource.
+// In publish mode, use a connection string representing an external SQL Server instance.
+IResourceBuilder<IResourceWithConnectionString> db = builder.ExecutionContext.IsRunMode
+    ? builder.AddSqlServer("sql").AddDatabase("db")
+    : builder.AddConnectionString("db");
 
 var insertionRows = builder.AddParameter("insertionRows");
 
@@ -640,9 +642,11 @@ import { createBuilder } from './.aspire/modules/aspire.mjs';
 
 const builder = await createBuilder();
 
-const sql = await builder.addSqlServer('sql');
-await sql.publishAsConnectionString();
-const db = await sql.addDatabase('db');
+// In run mode, add the actual SQL Server resource.
+// In publish mode, use a connection string representing an external SQL Server instance.
+const db = builder.executionContext.isRunMode
+    ? await builder.addSqlServer('sql').then(sql => sql.addDatabase('db'))
+    : await builder.addConnectionString('db');
 
 const insertionRows = await builder.addParameter('insertionRows');
 
@@ -663,12 +667,11 @@ The following steps are performed:
 
 <Steps>
 
-1. Adds a SQL Server resource named `sql` and publishes it as a connection string.
-2. Adds a database named `db`.
-3. Adds a parameter named `insertionRows`.
-4. Adds a project named `api` and associates it with the `Projects.Parameters_ApiService` project resource type-parameter.
-5. Passes the `insertionRows` parameter to the `api` project.
-6. References the `db` database.
+1. In run mode, adds a SQL Server resource named `sql` and a database named `db`. In publish mode, uses an external connection string named `db`.
+2. Adds a parameter named `insertionRows`.
+3. Adds a project named `api` and associates it with the `Projects.Parameters_ApiService` project resource type-parameter.
+4. Passes the `insertionRows` parameter to the `api` project.
+5. References the `db` database.
 
 </Steps>
 

src/frontend/src/content/docs/integrations/cloud/azure/overview.mdx

@@ -118,13 +118,24 @@ The following table summarizes the naming conventions used to express Azure reso
 
 | Operation | API | Description |
 |--|--|--|
-| Publish | `PublishAsConnectionString` | Changes the resource to be published as a connection string reference in the manifest. |
+| Publish | `PublishAsConnectionString` _(obsolete)_ | Changes the resource to be published as a connection string reference in the manifest. Use `AddConnectionString` with the [execution context](/get-started/app-host/) instead. |
 | Publish | `PublishAsExisting` | Uses an existing Azure resource when the application is deployed instead of creating a new one. |
 | Run | `RunAsContainer` | Configures an equivalent container to run locally. For more information, see [Local containers](#local-containers). |
 | Run | `RunAsEmulator` | Configures the Azure resource to be emulated. For more information, see [Local emulators](#local-emulators). |
 | Run | `RunAsExisting` | Uses an existing resource when the application is running instead of creating a new one. |
 | Publish and Run | `AsExisting` | Uses an existing resource regardless of the operation. |
 
+:::caution[PublishAsConnectionString is obsolete]
+`PublishAsConnectionString` is obsolete as of .NET Aspire 9.5. It only changes the manifest representation and has no effect on other publishers. To express different run and publish behavior, use [`AddConnectionString`](/fundamentals/external-parameters/#connection-string-values) with the execution context:
+
+```csharp
+var resource = builder.ExecutionContext.IsPublishMode
+    ? builder.AddAzureServiceBus("messaging")
+    : builder.AddConnectionString("messaging");
+```
+
+:::
+
 <Aside type="note">
 Not all APIs are available on all Azure resources. For example, some Azure resources can be containerized or emulated, while others can't.
 </Aside>

src/frontend/src/content/docs/ja/fundamentals/external-parameters.mdx

@@ -517,9 +517,11 @@ builder.AddProject<Projects.AspireReferenceExpressions_CustomerAPI>("customerapi
 ```csharp title="AppHost.cs"
 var builder = DistributedApplication.CreateBuilder(args);
 
-var db = builder.AddSqlServer("sql")
-                .PublishAsConnectionString()
-                .AddDatabase("db");
+// 実行モードでは実際の SQL Server リソースを追加します。
+// 発行モードでは外部 SQL Server インスタンスを表す接続文字列を使用します。
+IResourceBuilder<IResourceWithConnectionString> db = builder.ExecutionContext.IsRunMode
+    ? builder.AddSqlServer("sql").AddDatabase("db")
+    : builder.AddConnectionString("db");
 
 var insertionRows = builder.AddParameter("insertionRows");
 
@@ -557,12 +559,11 @@ await builder.build().run();
 
 <Steps>
 
-1. `sql` という名前の SQL Server リソースを追加し、接続文字列として公開します。
-2. `db` という名前のデータベースを追加します。
-3. `insertionRows` という名前のパラメーターを追加します。
-4. `api` という名前のプロジェクトを追加し、それを `Projects.Parameters_ApiService` のプロジェクト リソース型として関連付けます。
-5. `insertionRows` パラメーターを `api` プロジェクトに渡します。
-6. `db` データベースを参照します。
+1. 実行モードでは `sql` という名前の SQL Server リソースと `db` という名前のデータベースを追加します。発行モードでは `db` という名前の外部接続文字列を使用します。
+2. `insertionRows` という名前のパラメーターを追加します。
+3. `api` という名前のプロジェクトを追加し、それを `Projects.Parameters_ApiService` のプロジェクト リソース型として関連付けます。
+4. `insertionRows` パラメーターを `api` プロジェクトに渡します。
+5. `db` データベースを参照します。
 
 </Steps>