Add public/private visibility for trees

- Add is_public field to Tree model (private by default)
- Update access control: users see default trees, public trees, or their own
- Update all tree endpoints (list, search, get, categories) with new visibility logic
- Default/system trees are automatically marked as public
- Add migration 004 to add is_public column and update existing defaults
- Fix pydantic settings to ignore extra env vars (DATABASE_URL_SYNC)

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

backend/app/models/tree.py

@@ -31,6 +31,7 @@ class Tree(Base):
         index=True
     )
     is_active: Mapped[bool] = mapped_column(Boolean, default=True)
+    is_public: Mapped[bool] = mapped_column(Boolean, default=False, index=True)
     is_default: Mapped[bool] = mapped_column(Boolean, default=False, index=True)
     version: Mapped[int] = mapped_column(Integer, default=1)
     created_at: Mapped[datetime] = mapped_column(