Looks like it is the power settings you’re talking about

https://support.google.com/mail/thread/4171361/the-gmail-and...

If you’re looking for gmail, it’s up to google to handle pushing notifications. This should be happening through firebase, but it will be the same on any platform/OS. If they’re not pushing emails on arrival, you won’t see messages.

If you’re not using some sort of push notification, as with another app, you’ll have to use polling which means that you’ll only get new messages each time the app polls the server.