I'm lucky enough to close my phone as long as I want, even it's stressful. Whenever I open it I saw same messages over and over again, where are you, call me back. 99% of those has no importance in my life. I just need to connect to internet time to time while I was out, that's why I get out of plane mod. But still getting those messages, mails, I kinda feel guilty for not turning back to some of them but freaking technology is a big snitch. "Oh he opened his phone, oh he opened that app, oh he's still not replying to you!."
I'm not a popular guy so I have no trouble on discord I don't even know if it has a sound notification, all the servers already muted but one. That's where I'm always on, and nothing is popping from nowhere.
And I feel you about sleep cycles, it sucks. Being tired all the time, having occasional pains out of nowhere, It's all there even without notifications.
Ah, I don't even get messages on my phone :D Only on Whatsapp and only by one person (I haven't had my phone for long and very few people have my number, and most of them live with me, soo...)
I try to respond to every message. If it's spammers, I block them. If it's friends or people in need of help, I answer or try to help them. Fortunately for me in this case, I am not very popular, so I get very few of these too. But I do feel an urge to respond ASAP to my friends because I have been in need before and know that it's annoying if a good friend is not picking up the phone just out of laziness or annoyment.