Sync is back on the Play Store, but it's not a third-party Reddit app anymore
(www.androidpolice.com)
which implies using an external API to do that translation
It doesn't. You can have local models.
Storing cloud backups requires a server and storage, etc.
Yes, it doesn't have to be the author's storage. Many, many apps implement it as adding the data to your Google Drive / Dropbox / whatever.