You have some custom attributes that you are looking to hide so that users won't be able to see them when attempting to configure project list in Classic with additional fields.
You tried moving those attributes under Project-Admin page and securing admin page via security groups but didn't seem to work as you ensured Attribute Value Protection was checked.
All Clarity versions.
As per the current functionality it is not possible to make attributes not be available in Classic when attempting to configure Project List with additional columns. This functionality is only available in Modern UX by using Field level security.