test: implement comprehensive test strategy

- Add Playwright for E2E testing with auth.spec.ts
- Add dialog component tests (8 test cases)
- Add sidebar component tests (11 test cases)
- Add login page integration tests (11 test cases)
- Add dashboard page tests (12 test cases)
- Update package.json with e2e test scripts
- Configure Playwright for Chromium and Firefox
- Test coverage for UI interactions, auth flows, and navigation

admin-web/playwright.config.ts

@@ -0,0 +1,32 @@
+import { defineConfig, devices } from '@playwright/test'
+
+export default defineConfig({
+  testDir: './e2e',
+  fullyParallel: true,
+  forbidOnly: !!process.env.CI,
+  retries: process.env.CI ? 2 : 0,
+  workers: process.env.CI ? 1 : undefined,
+  reporter: 'html',
+  use: {
+    baseURL: 'http://localhost:3000',
+    trace: 'on-first-retry',
+    screenshot: 'only-on-failure',
+  },
+
+  projects: [
+    {
+      name: 'chromium',
+      use: { ...devices['Desktop Chrome'] },
+    },
+    {
+      name: 'firefox',
+      use: { ...devices['Desktop Firefox'] },
+    },
+  ],
+
+  webServer: {
+    command: 'npm run dev',
+    url: 'http://localhost:3000',
+    reuseExistingServer: !process.env.CI,
+  },
+})