Redesign the app shell, directory, and every page#38

Integrate registry setup and new-tab links with the refreshed page layouts

Preserve refreshed docs navigation and shared directory search after rebase

Redesign the contributors and sponsors pages

Rebuild the docs in the new style

Redesign the library detail page

Add CodeRabbit reviews badge to README

Remove library detail page background images

Document safe PowerShell output redirection

Add library backgrounds, registry setup guides, and new-tab links