You’re giving up your sleep, and by extension your health, to make someone else richer.
You should be pushing that you get the entire day off. And when your manager denies it, and they will because this doesn’t sound like a one-off emergency, insist that you need to call them and wake them up each and every time. If it truly is an emergency, they will be glad that you are keeping them in the loop. When it’s not (and it almost never is), they need to champion your need to make it stop.
Everyone involved needs to feel the pain for the harm they are causing.