Remove Product Hunt badge from landing page

[higgins]

Motivation

• Remove the Product Hunt badge UI from the public landing page and eliminate the now-unused badge component.
• Clean up imports and reduce UI clutter from a temporary/promotion element.

Description

• Removed the ProductHunt import and the <ProductHunt /> usage from app/page.tsx.
• Deleted the component file src/components/ProductHunt.tsx and its associated JSX/CSS.
• Adjusted the landing page layout to no longer render the floating Product Hunt badge.

Testing

• Started the dev server with npm run dev, which compiled the app (Google font fetches fell back due to network proxy but the app compiled).
• Ran a Playwright script to load http://127.0.0.1:3000 and capture a screenshot of the landing page, producing artifacts/landing-no-product-hunt.png successfully.
• No automated unit tests were present or run for this change.

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Codex Task