> It contains at the home directory the folder Sync which is what gets synced across all devices and what needs to be maintained.

That's a core Dropbox-level mistake of putting the backup cart before the main use horse - your files should be sorted according to their primary, not backup use

> Syncthing works very well, its only constraint is that it does need the devices to be often on if you want consistent syncing.

So it's working very poorly, this is a very inconvenient constraint

> phone is a whole other beast. It does not have enough storage to

Indeed

Overall, that fits the title perfectly, and is a bad way to setup your backups. Special needs need special apps.