Hicrosebr ,
Thanks for posting in Apple Support Communities.
When you choose to back up an app to iCloud, it backs up the app data, not the actual app. You can delete the app from one device and download it to another device. If you have an account in the app, it will likely need your login to show saved data.
If you've erased the other device and want to restore an iCloud backup that has this app data, then it will have the app data in the backup, but if it's an app that requires you to have some sort of account, you will need to sign in.
In order to complete the backup to iCloud, you simply need to have enough storage available or reduce the size of your backup.
Choose which apps to back up on your iPhone, iPad, or iPod touch
1. Go to Settings > [your name] > iCloud.
2. Tap Manage Account Storage or tap Manage Storage, then tap Backups.
3. Tap the name of the device that you're using.
4. Turn off any apps that you don't want to back up.
5. Choose Turn Off & Delete.
When you confirm that you want to Turn Off & Delete an app, it turns off iCloud Backup for that app and removes all of its information from iCloud.
Some apps are always backed up and you can't turn them off.
These steps can be found in Manage your iCloud storage - Apple Support.
Regards.