I lead the anti abuse team at Discord. I've looked into this case a bit more in-depth to see what was going on. Although I can't get into specifics, given the poster was kind enough to provide us with ticket IDs, I was able to look into this a bit further to see what actually triggered the account ban.
> Discord bans me for using their official client
This statement is false, unfortunately - and our abuse detection flagged the account for using our API in ways that our official clients do not. In this case, there was indeed a 3rd party client involved. Although our rules and heuristics do not specifically target 3rd party clients, it does target things that "don't look like what our official client does" which is very effective at targeting spambots that are constantly waging war against our platform - but has the unfortunate side-effect that using a 3rd party client in certain ways may lead to account termination.
In general, appealing the ban would lead to an unban (we're humans after all, and we're trying to stop spammers/bad actors, and that's what this system is meant to stop.) I am going to following up with our T&S team to understand why this case saw such a rocky conclusion.