test(e2e): establish website interaction baseline

[xingkaixin]

Summary

• run the Web app and marketing site as separate Playwright projects
• cover website copy success, fallback, failure feedback, and showcase navigation
• handle clipboard rejection without unhandled promises and announce failures through aria-live
• retain the existing Web search, keyboard, and detail-drawer coverage

Why

Critical website interactions had no browser-level regression coverage. The copy handler also treated a failed fallback as success and could leave an unhandled rejection.

Validation

• pnpm lint
• pnpm format:check
• pnpm build
• pnpm test
• pnpm test:e2e (6 passed)

Closes CS-41