Add post-build tests to GitHub Pages deployment

[G-Fourteen]

Summary

• add a structural smoke test that validates the chat UI and required scripts using jsdom
• wire the new test into the npm test script and dependencies
• update the GitHub Pages workflow to install dependencies and run the tests after the build step

Testing

• npm test

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https://chatgpt.com/codex/tasks/task_b_68c96163d1408329a1b390c469a329c6