Do you get the patron badge if your email address here is the same as your Patreon address, or do you have to log in through that account?
I think you need to log in to the forum with your Patreon account?
Documentation links (such as they are) are here: https://www.discourse.org/plugins/patreon.html
Yes, it looks like changing my email to match the Patreon account and then logging in through that gets the badge while keeping my history. Great!