The update is free. There should be a "You own this game" banner at the top of the page with a link to the downloads if you're logged in.
You can also access the downloads for any game you own on Itch through your library, which is located in the dropdown menu in the upper right, or through the Itch.io desktop app.
Or, hey, you could also access the downloads from the receipt you get in your email as well, but that seems a bit harder than the other options.