fix(theme): align docs chrome with main site

[joeliu926]

Summary

• align the docs search spacing and remove the VitePress sidebar curtain that clipped its top border
• remove the on-page outline rail and match the main-site three-state theme selector
• sync the animated SandBase brand mark and header logo spacing with the main site
• add vendor icons to footer social links and sync the Solutions footer links with the main site

Verification

• npm run build
• git diff --check
• browser-verified search border visibility, outline layout, theme states, logo sizing/animation selectors, social icons, and footer links