Overview
You are curious whether limited-access user permission lockdown mode be turned off without affecting Bonzai functionality. You previously attempted to add a documents section subfolder with unique permissions but ran into this situation where limited-access user permission lockdown mode needs to be turned off at the site level.
Information
Please note that you can turn it off but the Lockdown mode is on by default for all publishing sites, including if a legacy publishing site template was applied to the site collection. Lockdown mode is the recommended configuration if greater security on your sites is a requirement.
If you disable the limited-access user permission lockdown mode site collection feature, users in the "limited access" permissions level (such as Anonymous Users) can gain access to certain areas of your site.
Please refer to this article: Understanding the Permission level in SharePoint Online