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/user.py

@@ -1,11 +1,17 @@
 import uuid
 from datetime import datetime, timezone
-from typing import Optional
-from sqlalchemy import String, DateTime, ForeignKey
+from typing import Optional, TYPE_CHECKING
+from sqlalchemy import String, DateTime, ForeignKey, Boolean
 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.team import Team
+    from app.models.tree import Tree
+    from app.models.session import Session
+    from app.models.folder import UserFolder
+
 
 class User(Base):
     __tablename__ = "users"
@@ -19,6 +25,7 @@ class User(Base):
     password_hash: Mapped[str] = mapped_column(String(255), nullable=False)
     name: Mapped[str] = mapped_column(String(255), nullable=False)
     role: Mapped[str] = mapped_column(String(50), nullable=False, default="engineer")
+    is_team_admin: Mapped[bool] = mapped_column(Boolean, nullable=False, default=False)
     team_id: Mapped[Optional[uuid.UUID]] = mapped_column(
         UUID(as_uuid=True),
         ForeignKey("teams.id"),
@@ -38,4 +45,15 @@ class User(Base):
     # Relationships
     team: Mapped[Optional["Team"]] = relationship("Team", back_populates="users")
     trees: Mapped[list["Tree"]] = relationship("Tree", back_populates="author")
-    sessions: Mapped[list["Session"]] = relationship("Session", back_populates="user")
+    sessions: Mapped[list["Session"]] = relationship("Session", back_populates="user")
+    folders: Mapped[list["UserFolder"]] = relationship("UserFolder", back_populates="user")
+
+    @property
+    def is_admin(self) -> bool:
+        """Returns True if user is a global (Patherly) admin."""
+        return self.role == "admin"
+
+    @property
+    def can_manage_team(self) -> bool:
+        """Returns True if user can manage their team (team admin or global admin)."""
+        return self.is_admin or (self.is_team_admin and self.team_id is not None)