Add Trending Paper public page

[Dai818]

Summary

• add a read-only Trending Paper page at /ResearchStudio/trending-paper/
• mirror the latest public-facing UI from the internal Trending Paper page
• load published editions dynamically from the existing public editions API and refresh every 60 seconds
• keep the current Weekly/Daily controls, search, Voted/Date sorting, streamed cards, viewers, CTA, and responsive layout
• physically exclude Debug mode, regeneration, version history, HF comments, and all write requests

Validation

• JavaScript syntax check passed
• HTML and relative asset paths validated for GitHub Pages under /ResearchStudio
• browser-tested Weekly/Daily data loading, Date/Voted sorting, search, 4-card streaming, and Reel viewer
• verified the public bundle contains only two read-only GET requests
• verified no Debug, regeneration, version-history, comment, or write-request code is present
• verified the server API CORS and Reel/Poster CSP allow https://microsoft.github.io

This supersedes the older draft implementation in #32, which no longer matches the current UI.