Add Playwright e2e tests for game interactions

[moKshagna-p]

Feature: Add e2e tests for game functionality

The repo currently has zero tests. We should add Playwright-based e2e tests covering the core game interactions.

Scope

Falling Words game:

• Game starts on typing
• Enter restarts from idle/game-over
• Clicking game area refocuses input
• Tab navigates through header/footer links normally
• Game pauses on tab switch, resumes on return
• Window blur/focus pause/resume
• Word typing and submission
• Difficulty switching
• Game-over state and score display

Survival game:

• Game starts on typing
• Health system and damage
• Enter restarts
• Window blur ends game (production behavior — keep as-is)

Test structure

apps/frontend/e2e/
├── playwright.config.ts
├── fixtures/
│   └── game.ts          # shared helpers (start game, wait for game-over, etc)
├── falling-words/
│   ├── focus.spec.ts    # focus/click/tab/Enter behaviors
│   ├── pause.spec.ts    # visibilitychange pause/resume
│   └── gameplay.spec.ts # word typing, scoring, game-over
└── survival/
    └── gameplay.spec.ts

Infrastructure

• Install @playwright/test as dev dependency
• playwright.config.ts with webServer pointing at bun run dev
• CI integration (add to .github/workflows/ci.yml)