What is Microsoft 365 or Office 365 Push Notification Service?
From
https://learn.microsoft.com/en-us/exchange/configuring-push-...
How do I enable push notifications?
In order to enable push notifications, the on-premises Exchange 2013 servers must connect to the Microsoft 365 or Office 365 Push Notification Service to send push notifications to iPhones and iPads. Exchange 2013 on-premises servers route their update notifications through the Microsoft 365 or Office 365 notification services to remove the need for enrolling developer accounts with third-party push notification services.
So it goes like
1. Your server 2. Microsoft server 3. Apple server 4. Device
So this begs the next question: does Microsoft require warrants to disclose these notifications?
You may instead want to pcap a mobile client to see where the notification is coming from, I bet the server still phones home somehow. It's possible Apple exempted themselves from their notification policies and integrated their Exchange push services into the OS power manager like they did their APN service, but I'm not sure if I'd expect them to put in that much work for what's essentially a competitor.
As a side note, because it's not made clear during setup: the Outlook app for mobile phones will keep a copy of your email on Microsoft's servers (and a partial copy on the device); if you use that app, Microsoft will poll for updates the normal way and likely still push the notifications through Apple's servers, despite you not having set up any direct connection from your server to the cloud. This isn't the case for the built-in email clients, of course, but the Outlook app seems to be quite popular for Exchange accounts.