Does iCloud backup data from apps that are not designed to sync with iCloud?

I need to send in my iPad for repair, and want to know if iCloud backs up ALL app data, or only the apps that are designed to sync their data with iCloud?

An example is my 400 hour Slay the Spire save file. It doesn’t get synced to iCloud normally (so no cloud saves across devices). Does iCloud device backup back up the app data of such apps? If I erase the iPad, send it in for repair, and then restore from iCloud, will I get this save data back?

Yes, iCloud Backup does backup the data of apps that do not otherwise sync with iCloud.

If you erase the iPad, send it in for repair, and then restore from iCloud Backup, you will get the data for such app's back. Note that there are some exceptions, where the app developer has specifically requested that their data may not be backed up in iCloud. Usually this is authentication tokens, which means that you will have to login to the app once again after restoring from backup.