While the Sign-up Sheets plugin doesn’t have this specific features, you can still accomplish this by installing a plugin such as WP-Members which allows you to do just that. Once installed, just make sure to go to Settings > WP-Members and under the “Custom Post Types” section, check the box next to “Sign-up Sheets” which allows you to secure individual Sign-up Sheets to require you user to log in before accessing them.
Additionally, depending on how you wanted to list your sheets, you may also be able to leverage the “Category” feature of Sign-up Sheets Pro to have separate “Current Sheets” listings for both public and private events. You can create different categories for each and use the [sign_up_sheet]
shortcode or similar Gutenberg block to display just upcoming sheets in a specific category.