feat: restructure test infrastructure with unit/integration/system separation

Test Organization:
- Create tests/unit/, tests/integration/, tests/system/ directories
- Move existing tests into appropriate categories
- Add pytest markers (@pytest.mark.unit, @pytest.mark.integration)

Shared Fixtures:
- Create conftest.py with SQLite engine (for unit tests)
- Add PostgreSQL session fixture with transaction rollback
- Add TestClient fixture for API tests

Configuration:
- Update pyproject.toml with asyncio_mode=auto
- Add test markers and default addopts
- Add aiosqlite dependency for SQLite support

E2E Testing:
- Initialize Playwright in e2e/ directory
- Add playwright.config.ts
- Create login flow E2E test

Build:
- Add test-unit, test-integration, test-system, test-e2e to Makefile
- Update test target to run all categories
- Add testing documentation to README

Note: Some tests have import issues due to missing python-jose
package in dev environment. This needs to be addressed separately.

README.md

@@ -0,0 +1,53 @@
+
+## Testing Strategy
+
+The project uses a three-tier testing approach:
+
+### Test Categories
+
+1. **Unit Tests** (`apps/api/tests/unit/`)
+   - Fast tests with no external dependencies
+   - Use SQLite in-memory database
+   - Run with: `make test-unit` or `pytest -m unit`
+
+2. **Integration Tests** (`apps/api/tests/integration/`)
+   - Test API endpoints with database
+   - Use PostgreSQL with transaction rollback
+   - Run with: `make test-integration` or `pytest -m integration`
+
+3. **System/E2E Tests** (`e2e/`)
+   - End-to-end tests using Playwright
+   - Test full user journeys
+   - Run with: `make test-e2e`
+
+### Running Tests
+
+```bash
+# Run all tests (excludes system tests by default)
+make test
+
+# Run specific categories
+make test-unit          # Fast unit tests only
+make test-integration   # Integration tests with DB
+make test-system        # Full stack tests
+make test-e2e          # Browser-based E2E tests
+
+# Inside Docker container
+docker compose exec api pytest -v -m unit
+docker compose exec api pytest -v -m integration
+```
+
+### Test Markers
+
+Tests are marked with pytest markers:
+- `@pytest.mark.unit` - Fast, isolated tests
+- `@pytest.mark.integration` - Tests with database/external services
+- `@pytest.mark.system` - Full stack tests
+
+### Shared Fixtures
+
+Common fixtures are in `apps/api/tests/conftest.py`:
+- `sqlite_engine` - SQLite engine for unit tests
+- `postgres_engine` - PostgreSQL engine for integration tests
+- `db_session` - Database session with transaction rollback
+- `test_client` - FastAPI TestClient instance