feat: add AI chat builder frontend — types, API client, store, components, page, routing

- TypeScript types for chat session, messages, and responses
- API client module with all 6 endpoints
- Zustand store with session management, message sending, tree generation, import, resume
- 7 chat components: ChatMessage, ChatInput, ChatPanel, PhaseIndicator, ChatToolbar, EmptyPreview, StaticTreePreview
- AIChatBuilderPage with split-panel layout (60% chat / 40% preview)
- Route at /ai/chat with lazy loading
- "Build with AI" button on TreeLibraryPage
- Session resume via URL search params

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

frontend/src/components/ai-chat/ChatPanel.tsx

@@ -0,0 +1,47 @@
+import { useEffect, useRef } from 'react'
+import { ChatMessage } from './ChatMessage'
+import { ChatInput } from './ChatInput'
+import { Spinner } from '@/components/common/Spinner'
+import type { ChatMessage as ChatMessageType } from '@/types'
+
+interface ChatPanelProps {
+  messages: ChatMessageType[]
+  isResponding: boolean
+  onSendMessage: (content: string) => void
+  disabled?: boolean
+}
+
+export function ChatPanel({ messages, isResponding, onSendMessage, disabled }: ChatPanelProps) {
+  const scrollRef = useRef<HTMLDivElement>(null)
+
+  // Auto-scroll to bottom on new messages
+  useEffect(() => {
+    if (scrollRef.current) {
+      scrollRef.current.scrollTop = scrollRef.current.scrollHeight
+    }
+  }, [messages, isResponding])
+
+  return (
+    <div className="flex h-full flex-col">
+      {/* Messages */}
+      <div ref={scrollRef} className="flex-1 overflow-y-auto px-4 py-4 space-y-4">
+        {messages.map((msg, i) => (
+          <ChatMessage key={i} message={msg} />
+        ))}
+        {isResponding && (
+          <div className="flex items-center gap-2 text-sm text-muted-foreground">
+            <Spinner size="sm" />
+            <span>Thinking...</span>
+          </div>
+        )}
+      </div>
+
+      {/* Input */}
+      <ChatInput
+        onSend={onSendMessage}
+        disabled={disabled || isResponding}
+        placeholder={isResponding ? 'Waiting for response...' : 'Type a message...'}
+      />
+    </div>
+  )
+}