Add tree organization system with categories, tags, and folders

Features:
- Categories: Global and team-specific tree categorization (admin-managed)
- Tags: Flexible tree tagging with autocomplete (author + admin)
- User folders: Personal tree collections with subfolder support
  - Hierarchical structure (max 3 levels deep)
  - Right-click context menu for folder management
  - Cascade delete for subfolders
- Filter trees by category, tags, and folder in library view

Backend:
- New models: Category, Tag, UserFolder with relationships
- New API endpoints for categories, tags, and folders
- Tree organization migrations (005, 006)

Frontend:
- FolderSidebar with hierarchical folder tree
- FolderEditModal for create/edit with color picker
- AddToFolderMenu for quick tree organization
- TagInput with autocomplete and TagBadges display
- Updated TreeMetadataForm and TreeLibraryPage

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

backend/app/schemas/category.py

@@ -0,0 +1,58 @@
+from datetime import datetime
+from typing import Optional
+from uuid import UUID
+from pydantic import BaseModel, Field
+import re
+
+
+def slugify(name: str) -> str:
+    """Convert a name to a URL-safe slug."""
+    # Remove non-alphanumeric chars except spaces, convert to lowercase
+    slug = re.sub(r'[^a-zA-Z0-9 ]', '', name.lower())
+    # Replace spaces with hyphens
+    slug = re.sub(r' +', '-', slug.strip())
+    return slug
+
+
+class CategoryBase(BaseModel):
+    name: str = Field(..., min_length=1, max_length=100)
+    description: Optional[str] = None
+
+
+class CategoryCreate(CategoryBase):
+    team_id: Optional[UUID] = Field(None, description="Team ID for team-specific category. NULL for global.")
+
+
+class CategoryUpdate(BaseModel):
+    name: Optional[str] = Field(None, min_length=1, max_length=100)
+    description: Optional[str] = None
+    display_order: Optional[int] = None
+    is_active: Optional[bool] = None
+
+
+class CategoryResponse(CategoryBase):
+    id: UUID
+    slug: str
+    team_id: Optional[UUID] = None
+    display_order: int
+    is_active: bool
+    created_at: datetime
+    updated_at: datetime
+    tree_count: int = 0  # Computed field
+
+    class Config:
+        from_attributes = True
+
+
+class CategoryListResponse(BaseModel):
+    id: UUID
+    name: str
+    slug: str
+    description: Optional[str] = None
+    team_id: Optional[UUID] = None
+    display_order: int
+    is_active: bool
+    tree_count: int = 0
+
+    class Config:
+        from_attributes = True