If you want to make a published Studio.Design website unavailable to visitors, you can set your site to private. With this setting, anyone trying to access your site's URL will see a 404 page instead, preventing outside access to your site.
Steps
Open [Settings] from the dashboard of the site you want to update.
Select [General] from the menu on the left.
Click the three-dot menu [...] next to [Publish Status].
Click [Set to Private].
Review the notice, then click [Set to Private] again in the confirmation dialog.
Once the setting is applied, open the URL in a browser to confirm you see the 404 page. That completes the process.
Making individual pages private
If you'd like to make only certain pages private instead of the entire site, use the per-page publish settings instead.
Making your site public again
To make a private site public again, simply publish it as you normally would.
Open the design editor.
Click [Publish] in the top right to open the publish panel.
Click [Publish] in the top right of the publish panel.
For more details, check out these articles:
Note: Republishing a site with a custom domain
If you're using a custom domain, you'll need to reissue and reconnect your TLS certificate. It may take up to 72 hours for the changes to take effect and for your site to be republished.