Yeah the server only sends what the user is currently looking + plus a buffer around their view. There's no actual checkbox state on the client. When the user clicks a checkbox a depress animation is started and a request is made (which the server responds to with no data and a 204). The user then gets the html for the next view down a long lived SSE connection that started when they first loaded the page. Because, there's a long lived connection, it has really good compression. Same thing happens when the user scrolls. If they scroll far enough a new view is rendered.

The billion items themselves are just in a server on the backend, stored in a sqlite database.