feat: integrate Playwright for E2E testing and enhance testing framework

- Added Playwright for end-to-end testing in the `apps/web` module, including a new `login.spec.ts` for testing login functionality.
- Updated package.json to include Playwright dependencies and new test commands for E2E testing.
- Enhanced .gitignore to exclude Playwright test results and reports.
- Modified existing documentation to reflect the integration of Playwright and updated testing guidelines.
- Refactored test commands to streamline the testing process, including a dedicated command for E2E tests.

These changes improve the testing framework by providing robust E2E testing capabilities, enhancing the reliability and quality of the application.

package.json

@@ -22,6 +22,7 @@
     "lint": "turbo run lint",
     "format": "prettier --write \"**/*.{ts,tsx,md}\"",
     "test": "turbo run test",
+    "test:e2e:web": "pnpm --filter web test:e2e",
     "typecheck": "turbo run typecheck",
     "typecheck:web": "turbo run typecheck --filter=web",
     "typecheck:landing": "turbo run typecheck --filter=landing",