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/scripts/seed_trees.py

@@ -3336,8 +3336,9 @@ async def create_tree(client: httpx.AsyncClient, token: str, tree_data: dict) ->
                 print(f"  [SKIP] Tree '{tree_data['name']}' already exists (ID: {tree['id']})")
                 return None
 
-    # Mark as default/system tree
+    # Mark as default/system tree (public and visible to all)
     tree_data["is_default"] = True
+    tree_data["is_public"] = True
 
     # Create the tree
     response = await client.post(