I finally wanted to join the official discord server using the join link on: "https://e621.net/static/discord", sadly I only get the following error after I authorized the e621 joiner application:

You don't have the permission to access the requested resource. It is either read-protected or not readable by the server.

I haven't previously been on the server, and the discord account is fairly new, so I can rule out a ban for this account.
Just to be sure, I waited 3 days and tried it again, but every time I try, I just get the above-mentioned 403 HTTP error.

Does anybody else have this issue, or do I just have to wait a bit longer for a manual approval of my account?

There are a few possible reasons. I have sent you a message.