Discord stores all messages and media.
I mean, how else do you think they can make it so all your existing chats show up when you log into your account from a different device? Signal stores all your messages and media as well, the difference is they encrypt it on their servers. Discord doesn't.
If you delete it, or delete your account, its still there.
That's more problematic, and there should honestly be a law against that. Come to think of it, doesn't that violate the GRDP? Either they have to treat their EU customers differently when it comes to this, or there's a lawsuit waiting to happen. In the former case, you might be able to force them to delete your data by using a VPN to pretend you're in Europe.