Push notifications need to connect to that many devices every hour easily

You may not get a notification every hour, but the phone still have to connect to Google APIs to check to know that.

You can say same thing about say location services, every phone if powered and connected to the internet would ping more than one an hour, more than billion devices are definitely online at any give time, not just Android phones, also every android TV, tablet, watch, and the hundreds if not thousands of other devices running GMS on top of AOSP .

There are probably few other APIs in GMS that would ping at least once an hour each device that is powered on, perhaps things like NTP for timing alerts or Emergency Alerts etc.

You may consider them "Background Services" , most of them however have some foreground UI if they need to, and users will notice if they don't work

There are roughly 5 billion smartphone users now, those devices are almost always on and sending background data somewhere. By volume, more of that data guess to Google than anybody else, on the order of hundreds of network requests per device, per hour.