I thought that programs simply didn't have these kinds of permissions.
I'm a security freak and things like this egregiously irritate me; software these years is also actively trying to encroach in my opinion. Websites want to show me notifications (for whatever stupid reason), and finding out discord has permissions and the ability to see what I'm doing is incredibly unnerving...
What can I do about this individually and also generally...?
Its almost as if you agreed to those terms when you installed discord. But you didnt read the end user agreement, did you?
Most people dont have an issue with discord knowing, and displaying certain programs under your name, in fact most of the people using it are gamers and like having people know what game they are in, so they include it as a feature.
If you are that concerned about the access to programs, you should just choose a platform that doesn't do it.