Extract shared rendering (chat-render.ts) and streaming hook
(use-chat-stream.ts) from ChatWidget so both the floating panel
and the new page share identical markdown/KaTeX/SSE logic.
New page features:
- Responsive sidebar (inline desktop, Sheet drawer mobile)
- Conversation search/filter
- Notebook picker via cmdk command palette
- Auto-growing multi-line textarea input
- Pop-out button on widget header to open /chat
ChatLayout.astro omits the floating widget to avoid duplicate UI.
Chat store gains selectedNotebookId for page-level notebook context.
shadcn-ui primitives (ScrollArea, Sheet, Command, Popover, etc.)
wired to existing SpiceBook dark theme tokens.
