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APKs can be end-to-end signed with keys under developer control. You can move between app stores or no store (data is preserved on update with same key). And Google can't fuck with it. (Well, they can fuck with the entirety of the rest of the phone, so that point's kinda moot.)
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On devices integrating Play services / Play Store as part of the partnership program they can do an unattended app install / uninstall and they can also obtain app data for most apps due to being one of the hard-wired allowed backup services. They provide core OS components too.
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Stuff like the package installer / permission controller, app runtime, etc. on their partner devices are provided via APEX components built by Google and shipped via the Play Store. Only people truly impacted by this are people using devices without Play getting apps from Play.