How does this work on a high level? If the server never sends the content, how can a client-side extension get it? Do most website just hide this on the frontend?
It removes the popup elements that cover the page and other little tricks.
The common key thing across all of them, though - the server is sending the content, and then a little JS payload that creates the popup asking you to pay.
It's not a particularly good way of protecting the content of the article, for obvious reasons.