feat(game): update websocket URL configuration and improve game room logic
- Change VITE_GAME_WS_URL from /api/v1/ws to /ws in .env.development
- Update proxy configuration in vite.config.ts to match new websocket path
- Refactor leave room functionality to properly disconnect websocket
and destroy room state
- Add e2e testing script to package.json
```
fix(backend): resolve merge conflicts and update API proxy configuration
- Remove leftover merge conflict markers from ChengduGamePage.vue
- Fix broken HTML structure by properly closing header and section tags
- Update proxy configuration to point to correct backend port (19000)
- Clean up import statements and remove conflicting code blocks
```
