Apple Mail isn't notifying until I open the app

Good evening,

For some reason, Apple Mail isn't notifying me of the emails I receive as it should. It's not until I open the app that I receive them. Opening the app and letting it run in the background doesn't seem to work either.

Notifications and the Mail app are both configured by default; I haven't tweaked anything except for the ding sound and the banner style, which is set as persistent. Everything else is either by default or activated. Other email apps such as Gmail seem to work just fine. I also have just one iCloud account for the Email app, and push is enabled (fetch is set to automatic).

I can't remember the last time I received a Mail notification without having to open the app myself, so I don't think it's an iOS update that messed with it. I'm not sure though...

Some other extra information that I don't know if it's relevant, but I can provide: I'm using an iPhone X, I've got privacy protection activated, I'm using private relay, and no, I don't have battery saver or focus mode activated.

Any idea how to fix this? ~Thanks a lot in advance.