auto-claude: subtask-5-2 - Create main Chatbot component with floating UI and message handling

- Created Chatbot.tsx with floating chat bubble UI
- Implemented streaming SSE message handling
- Added visitor ID persistence via localStorage for session continuity
- Integrated with /api/chat endpoint for AI responses
- Added suggested prompts for empty chat state
- Implemented error handling with retry functionality
- Added clear chat functionality
- Created responsive design with mobile support
- Created index.ts barrel export for chat components

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

src/components/chat/index.ts

@@ -0,0 +1,7 @@
+/**
+ * Chat components barrel export
+ */
+
+export { Chatbot } from './Chatbot';
+export { ChatMessage, TypingIndicator, WelcomeMessage } from './ChatMessage';
+export type { ChatMessageData, ChatRole } from './ChatMessage';