> I don't think the situation would have played out this way if I hadn't used Discord.
I have to disagree. Your students probably would have connected on Discord or another chat service anyways (even before the pandemic/lockdowns!), and they would have made the same comments, except you would not have heard them.
Source: current student (though not in university).
> Nevertheless, this experience took a pretty serious emotional toll on me. It's hard to feel like you're letting your students down.
I want you to know that especially among younger people such as myself, complaining (or "venting") is often used as a way of releasing stress after an exam. I don't think you should take it personally. Frankly, you sound like an incredible teacher for caring about your students' feedback about the exam, however misguided.
EDIT: I should add, the fact that your students felt comfortable complaining about your exam on your server, and not elsewhere, is a result of your inclusiveness (which is apparent in the actions detailed in your post).