I'm newish to Discord. I joined in around January or so. The first time I put myself on Invisible, which was recently, I thought "Oh cool I can access Discord, still get messages and do everything." But that's wrong and misleading.
It took me two to three searches, after a moment when the person I needed to access during a very bad time was not there because of the Status, to find out that the Invisible Status mutes notifications of messages you send to your friends/people in DMs. This means your friends won't see any notifications from the messages you send. At all.
Why is this information not put in the description in the part where you change your status? You can't actually access all of Discord, that is misleading.
At the very least, have the information available there. Don't make other people go through what I did when they needed a person to respond and because information was not available, they didn't get it.
You could also have a toggle setting for friends or strangers to reviece Notifications from you when you're set as Invisible.