One Site as a part of Multisite to be hidden (Un-published) from Public?

There are a few options for this:

Premium Plugins:

• This works well to help multisite set ups hide sites and gives you a few ways to do it - but it is not free: https://premium.wpmudev.org/project/sitewide-privacy-options-for-wordpress-mu/

• a good "coming soon" and "maintenance mode" plugin: https://www.seedprod.com/

Open Source Plugins:

• https://wordpress.org/plugins/wp-maintenance-mode/

• https://wordpress.org/plugins/password-protected

Custom:

• If the site uses a unique theme or child theme, one way is to create an empty file called index.html and store it in the root directory of your sub site. That should work because index.html will be displayed in place of index.php, which is what WordPress uses.

After seeing your clarification in the original question:

Every page inside the subsite you're trying to "hide" would need to be set so that only users with the permission level of "Admin" can see the page.

Anyone will be able to see that the page exists. Users are not logged in or are logged in but don't have the correct permission level that land on the restricted pages will receive a "This page is restricted" notification, where users that are logged in and have the appropriate permission level will be able to see all content within the page.