test: add xUnit test coverage for API controllers and client services

Create ChatAgent.Api.Tests and ChatAgent.Client.Tests projects with xUnit
and Moq. Test HealthController (200 + valid response), ChatController
(SSE streaming with mocked upstream, error handling), and ChatApiClient
(delta parsing, error events, health endpoint). 6 tests, all passing.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

src/ChatAgent.Api/Program.cs

@@ -66,3 +66,8 @@ app.UseAuthorization();
 app.MapControllers();
 
 app.Run();
+
+// This partial class declaration makes the auto-generated Program class public,
+// which is required by WebApplicationFactory<Program> in integration tests.
+// Without this, the test project cannot reference the entry point type.
+public partial class Program { }