I'd like my Discord online status to be set to offline rather than idle when my PC is set to Hibernation Mode.

I think that would only make sense as Hibernation Mode on a PC is very similar to turning it off, which also sets you to offline. In Hibernation Mode, you in fact don't get notifications and essentially have to boot it up in order to use it again. I typically use it when I'm asleep, whereas when I want to let my PC use less power during the day, I just have it set to Sleep Mode, as there's no boot time involved with that.