Add chat widget to docs site: floating panel for Q&A + live celestial queries
Floating chat panel injected via Starlight Head override:
- ChatWidget.astro wrapper with astro:after-swap for View Transitions
- ~900-line TypeScript widget: SSE streaming, conversation persistence
(localStorage), markdown rendering (marked + DOMPurify), suggestion
pills, two-click delete, conversation history, rAF-throttled streaming
- ~680-line CSS: dark/light themes (amber/slate palette), full-screen
mobile layout with FAB/Ask button overlap fix, reduced-motion support
- Three domain-specific suggestions: "Where is Jupiter right now?",
"How do I predict satellite passes?", "What functions handle rise/set
prediction?"
- FAB uses orbit SVG icon (3 rotated ellipses + center circle)
- Wired to /api/chat/stream endpoint (search backend)