Having switched phones a couple of months ago, there didn't seem to be a good option. Either you need to have root - which means that most banking apps won't work anymore -, you need to backup to the cloud which a) not every app supports and b) I don't want to do for more private data, or you need to use the backup API that however some apps also don't support.
It's a mess and I don't understand that Google hasn't fixed that.
What’s wrong with their built in support?
https://support.google.com/android/answer/2819582?hl=en
It doesn’t work like iCloud where everything is backed up - even private app data?
Which apps doesn’t it work with that you think it should?
I am looking through my apps and most of them are clients for server side functionality or productivity apps that use iCloud Drive, OneDrive or Google Drive.
Google Photos would take care of videos and photos and Contacts and calendars use standard syncing protocols.
Going from a Samsung to a new Samsung is easy. But if you switch between brands yeah it gets difficult.