I think its important to add the fact that App Center Push, Auth and Data are now being retired, despite Push being a fantastic offering IMO:
https://visualstudiomagazine.com/articles/2020/02/14/app-center-mbaas.aspx
"We are discontinuing efforts in the Auth, Data, and Push services and
working to retire these preview services in App Center," said John
Wargo, principal program manager for Visual Studio App Center. "With
this change, we will focus App Center on delivering a world-class
mobile and desktop DevOps experience. We will also work together with
Azure teams to help migrate developers to the native Azure services,
and ensure that Azure continues to be a great platform for your mobile
apps."
There seems to be no full migration path at time of writing, but there is the hint this will be handled mostly for existing users -
https://docs.microsoft.com/en-us/appcenter/migration/push/
We don’t expect customers to manually migrate from App Center Push to
Azure Notification Hubs; so before the service shutdown, we’ll provide
detailed instructions for how to streamline your app’s migration from
App Center Push to Azure Notification Hubs.