Replace JUST-OS iframe with native chat client using API (#702)

Replace the iframe-based JUST-OS chatbot integration with a native chat
client that communicates directly with the JUST-OS API at
bot.just-os.org/chat. This resolves several UX issues with the iframe
approach: conversation loss when switching between widget sizes, no
control over styling, and hacky negative margins to hide the JUST-OS
page header.

Key changes:
- New JS chat client (static/js/just-os-chat.js) that streams responses
  via newline-delimited JSON from the JUST-OS API
- Two display modes: docked right panel (default, 1/3 width) and
  floating centered panel (pop-out, resizable via drag handle)
- Session persistence via sessionStorage - conversation survives
  same-tab page navigations
- Welcome message on first open
- Bot responses rendered as HTML with inline citations shown as plain
  text and a collapsible reference list below each response
- Copy-to-clipboard button on bot messages
- New Chat button to reset conversation
- Full-page mode on /just_os_chatbot/ page works independently

Relates to #521

Co-authored-by: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
Co-authored-by: Richard Dushime <45734838+richarddushime@users.noreply.github.com>

Author: 3 people