Your old account is the one that is banned, the new one is not banned. However, I imagine that might've happened is that Discord automatically does an IP ban when you get banned and since you're the owner of both accounts, then your IP would now be banned.
You can just try and join the server again via the link on the Itch.io page. If it doesn't work, then it seems like your IP got banned.
EDIT: I looked into it and when you get banned from a Discord server, your IP also gets banned it seems.