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/pages/TreeLibraryPage.tsx

@@ -1,6 +1,6 @@
 import { useEffect, useState, useCallback, useMemo } from 'react'
 import { useNavigate, useSearchParams } from 'react-router-dom'
-import { X, RotateCcw, Play } from 'lucide-react'
+import { X, RotateCcw, Play, Sparkles } from 'lucide-react'
 import { treesApi } from '@/api/trees'
 import { categoriesApi } from '@/api/categories'
 import { foldersApi } from '@/api/folders'
@@ -272,11 +272,22 @@ export function TreeLibraryPage() {
               </p>
             </div>
             {canCreateTrees && (
-              <CreateFlowDropdown
-                aiEnabled={aiEnabled}
-                onOpenAIBuilder={() => setShowAIBuilder(true)}
-                label="Create New"
-              />
+              <div className="flex items-center gap-2">
+                {aiEnabled && (
+                  <button
+                    onClick={() => navigate('/ai/chat')}
+                    className="flex items-center gap-2 rounded-lg bg-gradient-brand px-4 py-2 text-sm font-medium text-white shadow-lg shadow-primary/20 hover:opacity-90 transition-opacity"
+                  >
+                    <Sparkles className="h-4 w-4" />
+                    Build with AI
+                  </button>
+                )}
+                <CreateFlowDropdown
+                  aiEnabled={aiEnabled}
+                  onOpenAIBuilder={() => setShowAIBuilder(true)}
+                  label="Create New"
+                />
+              </div>
             )}
           </div>