You do realize each app has to have its own notification server anyway? If anything this would use the same amount of battery because those apps just update when the store is refreshed(Like literally every app you have if you don’t disable it)
no. completely wrong. you don't understand. each app's backend service sends push notifications to apple's push notification servers and Apple aggregates all notifications to the phone so the phone only needs to run one notification service. the background service delivers notification to each app on your phone.
a "microsoft store app" will not have entitlements to send notifications to apple's push notification servers. user will need to run "Microsoft push notification service" in the background.