I just wanted to share that you can disable google play store on stock Android and not lose that much functionality, if for any reason you use an app that require Google play store or you want to make a play store purchase, you can enable it again.
I personally disabled it and I get my apps from Aurora Store, ApkPure and Droidify.
It decreased my phone battery usage by a lot and I am less dependent on google overall.
Not sure, whether it is relevant for this thread, but my phone (POCO F3) does not get any notifications if Google Play Services has no access to the internet. I scratched my head for a while to find out, why I never got them on mobile data. Not sure, what it does, if you disable the store.
Yeah, push is a play services thing.