You don't need to purchase license for each device, instead the license can be shared among your Android devices (including Chromebooks) or among your iOS devices.
But the license is not compatible between Android and iOS.
To restore the license information, navigate to [Home] > [Setting > [License], then hit the [Restore] button.
The license information is related to the Google Play or App Store account. So, it is very important that you login to Google Play or App Store with the same account that you had purchased the license to retrieve the purchased license information.
Can not restore the license....?
For Android user
In the device's [Setting] > [Accounts & Users] > Google type accounts, if you have multiple Google account registered there, firstly please make sure the Google Play uses the right account.
Please see [Switch Accounts in Google Play App] section in following link.
if it still didn't work, please temporarily remove the Google accounts except the one you purchased the license, then try to restore the license from the app.
For iOS user
Please check if the device recognizes the subscription license, see following for the detail.