docs: redesign README and Pages homepage

[recrack]

Summary

• redesign the repository README around the real SideRefresh renewal loop and product proof
• apply the same visual system to English, Korean, Japanese, and Simplified Chinese GitHub Pages routes
• add a public homepage design contract to local hooks, CI, and the Pages workflow

Verification

• Scripts/test-public-homepage-design.sh
• full .githooks/pre-push suite: Python 10, Swift 335, samples, Headless, public-source, Product Hunt asset/site, and Pages publication checks
• actionlint, shellcheck, and git diff --check
• desktop 1440 px and mobile 320/375/390 px visual checks

Boundaries

• the shown app state remains labelled as synthetic sample data
• no signed binary, GitHub Release, tag, Product Hunt launch, or custom domain change

Closes #14