Question: If I want to show a client some changes I made to the website in the staging area, is it possible for them to access this in some way, while still hiding this area for the public and search engines?
Answer: Yes, this is possible. You can either give your client administrator permissions to log in to the staging site or you assign the customers non-administrator user account to a certain user role like “clients”. In WP Staging settings you then can give this user role access to the staging site.
To create a new WordPress user role you can use this popular plugin.