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/models/folder.py

@@ -0,0 +1,93 @@
+import uuid
+from datetime import datetime, timezone
+from typing import TYPE_CHECKING, Optional
+from sqlalchemy import String, DateTime, ForeignKey, Integer, UniqueConstraint, Table, Column
+from sqlalchemy.orm import Mapped, mapped_column, relationship
+from sqlalchemy.dialects.postgresql import UUID
+from app.core.database import Base
+
+if TYPE_CHECKING:
+    from app.models.tree import Tree
+    from app.models.user import User
+
+
+# Junction table for folder-tree many-to-many relationship
+user_folder_trees = Table(
+    'user_folder_trees',
+    Base.metadata,
+    Column('folder_id', UUID(as_uuid=True), ForeignKey('user_folders.id', ondelete='CASCADE'), primary_key=True),
+    Column('tree_id', UUID(as_uuid=True), ForeignKey('trees.id', ondelete='CASCADE'), primary_key=True),
+    Column('added_at', DateTime(timezone=True), nullable=False, default=lambda: datetime.now(timezone.utc)),
+    Column('display_order', Integer, nullable=False, default=0)
+)
+
+
+class UserFolder(Base):
+    """User-specific folders for organizing trees.
+
+    - Each folder belongs to a single user
+    - Trees can be in multiple folders (like labels/tags)
+    - Folders are purely organizational - they don't affect tree visibility or permissions
+    """
+    __tablename__ = "user_folders"
+    __table_args__ = (
+        # Allow same name under different parents
+        UniqueConstraint('user_id', 'name', 'parent_id', name='uq_user_folders_user_name_parent'),
+    )
+
+    id: Mapped[uuid.UUID] = mapped_column(
+        UUID(as_uuid=True),
+        primary_key=True,
+        default=uuid.uuid4
+    )
+    user_id: Mapped[uuid.UUID] = mapped_column(
+        UUID(as_uuid=True),
+        ForeignKey("users.id", ondelete="CASCADE"),
+        nullable=False,
+        index=True
+    )
+    name: Mapped[str] = mapped_column(String(100), nullable=False)
+    color: Mapped[str] = mapped_column(String(7), nullable=False, default="#6366f1")
+    icon: Mapped[str] = mapped_column(String(50), nullable=False, default="folder")
+    display_order: Mapped[int] = mapped_column(Integer, nullable=False, default=0)
+    parent_id: Mapped[Optional[uuid.UUID]] = mapped_column(
+        UUID(as_uuid=True),
+        ForeignKey("user_folders.id", ondelete="CASCADE"),
+        nullable=True,
+        index=True
+    )
+    created_at: Mapped[datetime] = mapped_column(
+        DateTime(timezone=True),
+        default=lambda: datetime.now(timezone.utc)
+    )
+    updated_at: Mapped[datetime] = mapped_column(
+        DateTime(timezone=True),
+        default=lambda: datetime.now(timezone.utc),
+        onupdate=lambda: datetime.now(timezone.utc)
+    )
+
+    # Relationships
+    user: Mapped["User"] = relationship("User", back_populates="folders")
+    trees: Mapped[list["Tree"]] = relationship(
+        "Tree",
+        secondary=user_folder_trees,
+        back_populates="folders"
+    )
+    # Self-referential relationships for folder hierarchy
+    parent: Mapped[Optional["UserFolder"]] = relationship(
+        "UserFolder",
+        remote_side="UserFolder.id",
+        back_populates="children",
+        foreign_keys=[parent_id]
+    )
+    children: Mapped[list["UserFolder"]] = relationship(
+        "UserFolder",
+        back_populates="parent",
+        cascade="all, delete-orphan",
+        foreign_keys="UserFolder.parent_id"
+    )
+
+    @property
+    def tree_count(self) -> int:
+        """Returns the number of trees in this folder."""
+        return len(self.trees) if self.trees else 0