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>

openspec/changes/archive/2026-04-04-add-test-coverage/proposal.md

@@ -0,0 +1,26 @@
+## Why
+
+The project has zero test coverage. There are two controllers, a typed HttpClient service, and shared models — all untested. Adding tests now establishes the pattern before the codebase grows, and catches regressions as new phases are added.
+
+## What Changes
+
+- Create an xUnit test project for the API (`ChatAgent.Api.Tests`)
+- Create an xUnit test project for the Client services (`ChatAgent.Client.Tests`)
+- Add tests for HealthController (GET /api/health)
+- Add tests for ChatController (POST /api/chat SSE streaming proxy)
+- Add tests for ChatApiClient (GetHealthAsync, SendChatStreamingAsync)
+- Add both test projects to the solution
+
+## Capabilities
+
+### New Capabilities
+- `test-infrastructure`: Test project setup, test framework choices, and shared test utilities
+
+### Modified Capabilities
+<!-- None — adding tests doesn't change existing specs -->
+
+## Impact
+
+- `tests/ChatAgent.Api.Tests/`: New xUnit test project
+- `tests/ChatAgent.Client.Tests/`: New xUnit test project
+- `ChatAgent.sln`: Add test projects