You want to use “Restricted” visibility mode. This will only allow people who own the page to access it.
Check the guide here for more information: https://itch.io/docs/creators/access-control#visibility-modes/using-restricted
Thanks—that sounds promising! Nice that it blocks search engines too. But that official guide make it sound like I'd need to send every past user a download key or a password? It doesn't mention pre=existing owners being an exception. (And it doesn't say whether pre=existing owners will still see it when browsing their Library.) Maybe the docs are just unclear? Don't want to find out the hard way!
(Ideally pre=existing owners owners would even see it when they do a search—I know that's how I always go to my games—but I doubt that's possible.)
When someone pays for a game the system grants them a download key automatically, which represents their ownership of the product.
Check this guide here https://itch.io/docs/creators/download-keys