Whilst it makes sense to hid this group in the admin panel when managing users and groups, it needs to be shown on the Manage Permissions page.
This is for the case when you want to set permissions on an obecjt and don't want to have the inherited permissions. Since you can't edit inherited permissions, you have to remove them.
When you do that then there are no permissions, so you want to add Everyone back in as consumers. But it does not matter what you search for "everyone", "EVERYONE", "GROUP_EVERYONE", etc. it won't find the group.