Testing: Add Playwright E2E tests for interactive Web App games

[nishtha-agarwal-211]

Description

We need to expand browser automation test coverage for our interactive web projects to prevent visual and gameplay breakages.

Proposed Tasks

1. Create a Playwright test file (e.g., tic-tac-toe.spec.js or rock-paper-scissors.spec.js) inside web-app/tests-e2e/.
2. Write automated tests that cover:
   • Launching the project modal successfully.
   • Clicking game buttons (e.g. playing moves, rolling dice).
   • Verifying that game states update correctly (e.g. score changes, win conditions).
   • Verifying the reset board/game state button works.

[github-actions]

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