## 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