It's a Pixel. Starting with 9 or 10, Android limits apps' background activity unless they show a notification (and probably has limits for those too when the screen is off). Plenty of apps had to deal with this, I have four of these notifications.
These limits don't apply to notifications via Google's services (GCM or whatever they're currently called). So if you're using the Gmail app or another app for a specific mail service, sure you will receive push notifications quickly.
Interesting - I've not been able to reproduce this on a Pixel 3a or 4a 5G. FairEmail, with foreground notification, doesn't have any issues delivering notifications.
As you say, Google is making it a lot harder, but FE with a foreground notification seems to do this fine for me.
These limits don't apply to notifications via Google's services (GCM or whatever they're currently called). So if you're using the Gmail app or another app for a specific mail service, sure you will receive push notifications quickly.