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Phone Push Notifications: A Double-Edged Sword for User Privacy and Law Enforcement
(www.theregister.com)
This is a most excellent place for technology news and articles.
Depends on a lot of factors, maybe you're regaining that battery life elsewhere. But it is fact that several apps all doing their own thing will drain more battery than if they all relied on a single service like Firebase or UnifiedPush to wake them up
I haven't found a study that gives exact numbers. Maybe the difference in battery consumption will be 0.5%)