Make the research atlas searchable and scannable

[aruintelligence]

What changed

• Add a live search field, topic filters, result count, and empty state to the 13-lab research atlas.
• Arrange labs in responsive cards so visitors can scan titles and descriptions without a long banner stack.
• Keep the root and Pages homepage mirrored.

Verification

• Inline scripts parse; unique IDs; 13 labs tagged across 7 tool-call, 5 recipient, and 1 real-screen lab.
• node --test test/*.test.js (9/9 test files passed).
• Live search and filter inspection after Pages deployment.