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/category.py

@@ -0,0 +1,66 @@
+import uuid
+from datetime import datetime, timezone
+from typing import Optional, TYPE_CHECKING
+from sqlalchemy import String, Text, DateTime, ForeignKey, Boolean, Integer, UniqueConstraint
+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.team import Team
+    from app.models.user import User
+
+
+class TreeCategory(Base):
+    """Admin-managed categories for organizing trees.
+
+    Categories can be:
+    - Global (team_id=NULL): Created by Patherly admins, visible to all
+    - Team-specific (team_id set): Created by team admins, visible to team members
+    """
+    __tablename__ = "tree_categories"
+    __table_args__ = (
+        UniqueConstraint('slug', 'team_id', name='uq_tree_categories_slug_team'),
+    )
+
+    id: Mapped[uuid.UUID] = mapped_column(
+        UUID(as_uuid=True),
+        primary_key=True,
+        default=uuid.uuid4
+    )
+    name: Mapped[str] = mapped_column(String(100), nullable=False)
+    slug: Mapped[str] = mapped_column(String(100), nullable=False, index=True)
+    description: Mapped[Optional[str]] = mapped_column(Text, nullable=True)
+    team_id: Mapped[Optional[uuid.UUID]] = mapped_column(
+        UUID(as_uuid=True),
+        ForeignKey("teams.id", ondelete="CASCADE"),
+        nullable=True,
+        index=True
+    )
+    display_order: Mapped[int] = mapped_column(Integer, nullable=False, default=0, index=True)
+    is_active: Mapped[bool] = mapped_column(Boolean, nullable=False, default=True)
+    created_by: Mapped[Optional[uuid.UUID]] = mapped_column(
+        UUID(as_uuid=True),
+        ForeignKey("users.id", ondelete="SET NULL"),
+        nullable=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
+    team: Mapped[Optional["Team"]] = relationship("Team", back_populates="categories")
+    creator: Mapped[Optional["User"]] = relationship("User", foreign_keys=[created_by])
+    trees: Mapped[list["Tree"]] = relationship("Tree", back_populates="category_rel")
+
+    @property
+    def is_global(self) -> bool:
+        """Returns True if this is a global category (not team-specific)."""
+        return self.team_id is None