We apologize for the confusion.
First, about the iCloud backup used when switching devices: even without purchasing anything, if your device is set to back itself up to iCloud, the data in this app is backed up together with the rest of your device.
You can use this to transfer the app data when you switch devices.
The paid iCloud backup feature is a separate feature. Inside the app, it lets you create a backup of only this app's data in your own iCloud.
You create these backups manually. It is useful if you want to make frequent backups yourself, or if you want to transfer or sync data with another device such as an iPad.
Of course, you can also use it when switching devices, which makes the transfer easy.
In short: when switching devices, you can transfer your data for free with the standard iCloud backup, without purchasing anything.
With the paid iCloud backup feature, you can create backups as often as you like, which helps protect your data if your device is suddenly lost or fails, and lets you back up and restore easily at any time.
We hope you will consider it.