Stop the host when the single session server service finishes

Author: stephentoub

src/ModelContextProtocol/Hosting/SingleSessionMcpServerHostedService.cs

@@ -6,8 +6,18 @@ namespace ModelContextProtocol.Hosting;
 /// <summary>
 /// Hosted service for a single-session (e.g. stdio) MCP server.
 /// </summary>
-internal sealed class SingleSessionMcpServerHostedService(IMcpServer session) : BackgroundService
+internal sealed class SingleSessionMcpServerHostedService(IMcpServer session, IHostApplicationLifetime lifetime) : BackgroundService
 {
     /// <inheritdoc />
-    protected override Task ExecuteAsync(CancellationToken stoppingToken) => session.RunAsync(stoppingToken);
+    protected override async Task ExecuteAsync(CancellationToken stoppingToken)
+    {
+        try
+        {
+            await session.RunAsync(stoppingToken);
+        }
+        finally
+        {
+            lifetime.StopApplication();
+        }
+    }
 }