IMO any privacy consideration for storing per-app settings on the server could be mitigated by making this clear in the permission dialog.
"This app may store settings, drafts, or other information on this server" or similar.
I don't know if the idea is feasible in terms of separating different apps' settings storage. It seems preferable to me over a third party service though. I'd much rather have my instance store such stuff than, e.g., Google.