Mail app

iOS/iPadOS 15 and messaging app/no push/fetch notifications

Hi all,

I’m trying to figure out why email notifications are not arriving correctly.
So yesterday I deleted SparkMail from my iPhone and Mac and went to stock. Mac works great, new emails are automatically sent to the app and everything works as expected.

However, with my iPhone and my wife’s iPad, there seems to be no notification when the email arrives, like silently. I checked the notification settings and everything is enabled. Permissions are given, but nothing on the lock screen, no badge, and nothing on my watch. It seemed like the app wasn’t just checking for new emails, as I can hear an email coming in on Mac, but nothing happens on iPad and iPhone.
I started looking online, found there was such a thing as push and retrieve, and checked out what I had.

I really don’t understand how the mail app for iPad and iPhone works, as Gmail doesn’t even have a push option. I don’t understand the switch at the top and then the individual account options later. I also don’t automatically understand why it only works when the device is plugged in and on Wi-Fi.

Can someone explain to me how this app works or maybe a good alternative?
Why can’t it just push emails as they are received on the server? I remember, when I first tried the app, everything was flying, no issues.