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.

e2e/package.json

@@ -0,0 +1,13 @@
+{
+  "name": "headquarter-e2e",
+  "version": "0.1.0",
+  "private": true,
+  "scripts": {
+    "test": "playwright test",
+    "test:ui": "playwright test --ui",
+    "test:debug": "playwright test --debug"
+  },
+  "devDependencies": {
+    "@playwright/test": "^1.40.0"
+  }
+}