ICEBlock is making incredibly false privacy claims for marketing. They falsely claim it provides complete anonymity when it doesn't. They're ignoring both data kept by Apple and data available to the server but not stored. They're also spreading misinformation about Android:
https://www.iceblock.app/android
Their claims about push notifications on Android compared to iOS are completely false. Both Firebase Cloud Messaging (FCM) and the Apple Push Notification service (APNs) function in a similar way with similar privacy. However, Android does not force using FCM and apps can use other push systems.
iOS forces uses Apple services including getting apps through Apple where they have a record of which apps each person and account has installed and using their push notification service. Both FCM and APNs have tokens. Android doesn't allow apps to access device IDs. Push tokens aren't device IDs.
Apple and Google can identify devices/users based on push tokens obtained by law enforcement from services. Unlike Google, Apple only recently began requiring warrants:
https://www.reuters.com/technology/apple-now-requires-judges-consent-hand-over-push-notification-data-2023-12-12/
ICEBlock's claims about this are highly inaccurate and they haven't acknowledged corrections.