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.

.cursor/rules/testing.mdc

@@ -1,5 +1,5 @@
 ---
-description: TDD workflow, 80% coverage minimum, Vitest unit tests, and browser journey verification
+description: TDD workflow, 80% coverage minimum, Vitest unit tests, and Playwright E2E for apps/web
 alwaysApply: true
 ---
 
@@ -11,9 +11,9 @@ Test types:
 
 1. **Unit tests** — pure functions, transformers, validators, stores, utilities (`*.test.ts` / `*.test.tsx`, colocated or `__tests__/`)
 2. **Component tests** — Testing Library in packages that already have it (`packages/ui`, `packages/core-events`)
-3. **App journeys** — browser verification of `apps/web` flows (login, index / form / detail). There is no Playwright or NestJS E2E suite in this repo.
+3. **App journeys** — Playwright E2E in `apps/web/e2e/` (login is the first sample). Mock the backend with `page.route`; do not hit a live API unless the user asks. There is no NestJS/Supertest suite in this frontend repo.
 
-Runner: **Vitest**. Root command: `pnpm test`. Per-package: `pnpm --filter <pkg> test`. Also `pnpm typecheck` and `pnpm check:all`.
+Runner: **Vitest** for unit tests (`pnpm test`). Playwright for web E2E (`pnpm test:e2e:web` or `pnpm --filter web test:e2e`). Also `pnpm typecheck` and `pnpm check:all` (unit/lint/typecheck only).
 
 ## Test-Driven Development
 
@@ -30,11 +30,11 @@ MANDATORY workflow:
 
 1. Use **tdd-guide** agent
 2. Check test isolation
-3. Verify mocks are correct (`@repo/core-api` services, HTTP client — not a database)
+3. Verify mocks are correct (`@repo/core-api` / HTTP client for unit tests; `mockBackend` in `apps/web/e2e/fixtures/mock-api.ts` for Playwright)
 4. Fix implementation, not tests (unless tests are wrong)
 
 ## Agent Support
 
 - **tdd-guide** — Use PROACTIVELY for new features, enforces write-tests-first
-- **e2e-runner** — Frontend journeys: Vitest + Testing Library, plus browser verification for `apps/web`
+- **e2e-runner** — Playwright E2E in `apps/web/e2e/`, plus Vitest + Testing Library for package journeys
 - Skill: `.agents/skills/tdd-workflow/`