Set it up with your email accounts and go into settings and switch on "Google push mode" in "push settings" Turn off or even disable the gmail app and voila -- gmail push settings without syncing. The great thing about the XMPP Network is, there are a lot of other services you can get push notifications …
sync - Gmail app not displaying status bar notifications My Gmail would only receive emails when I manually entered the app and refreshed the screen. I googled how to fix and everything said sync Gmail, turn on notifications, delete cache and data, restart but nothing worked. Turns out my Battery optimization that's on constantly was preventing the push notifications. Why is android push notifications not working? Same Jan 17, 2020 Push email Outlook Android app - Microsoft Community
Jan 17, 2020
Delayed Gmail Notifications Could Be Caused By Doze Jul 17, 2020 Gmail Push frequency question, not - Android Forums Nov 18, 2019
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