feat: add rate limiting with countdown timer for docs chat

- Add in-memory rate limiter (10 requests/minute per user)
- Show informative message when limit reached explaining demo context
- Display countdown timer showing when chat becomes available again
- Auto-reset rate limit when timer expires
- Update documentation with rate limit FAQ and category selection flow

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

components/docs-chat/index.ts

@@ -2,5 +2,6 @@ export { DocsChatWidget } from './docs-chat-widget'
 export { ChatMessages } from './chat-messages'
 export { ChatInput } from './chat-input'
 export { ChatSuggestions } from './chat-suggestions'
+export { RateLimitMessage } from './rate-limit-message'
 export { useDocsChat } from './use-docs-chat'
 export type { ChatMessage } from './use-docs-chat'