It does have that. No idea why it wouldn't work for GP. If I lock my computer, or don't look at the Discord tab for a few minutes, my phone gets notifications.
Just to add my experience, I feel like it's hit or miss. It seems like I get notifications with zero issues. Then I'll randomly have a week or two in a row where I don't get notifications or get 50% of them. Not sure why this happens, but I use Discord as my only means of contact with multiple people.
Interesting. For what it's worth I am using Discord on Mac Safari (not TP), Win Chrome 69 (dev channel), and iOS. In one year I have not had any of the issues mentioned above. Perhaps using the desktop app can introduce problems.
Yeah it just doesn't work well for me or my friends we are always complaining. I don't know why and I don't really want to have nerd out with my chat app (just want it to work!).
As for using Slack, I am too scared of dropping 3am Friday/Saturday messages in my work chat instead of my group chat so keep separate apps.