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/playwright.config.ts

@@ -0,0 +1,25 @@
+import { defineConfig, devices } from '@playwright/test';
+
+export default defineConfig({
+  testDir: './tests',
+  fullyParallel: true,
+  forbidOnly: !!process.env.CI,
+  retries: process.env.CI ? 2 : 0,
+  workers: process.env.CI ? 1 : undefined,
+  reporter: 'list',
+  use: {
+    baseURL: process.env.WEB_URL || 'http://localhost:3000',
+    trace: 'on-first-retry',
+    screenshot: 'only-on-failure',
+  },
+  projects: [
+    {
+      name: 'chromium',
+      use: { ...devices['Desktop Chrome'] },
+    },
+    {
+      name: 'firefox',
+      use: { ...devices['Desktop Firefox'] },
+    },
+  ],
+});