It is a toggle. When it reads Publish Page the public page is rendered from the classic modules; clicking it switches it to Published (green) and immediately saves, so visitors now see the New Builder layout instead. Click again to unpublish and fall back to the module version. Because it auto-saves, make sure the canvas is in the state you want before toggling. When a page is already published with the builder, opening it in the admin lands you directly in the builder.