Currently I only sync across Windows PC-s.
I use my own Synology server for hosting it, and it's Synology Drive application for syncing. When there is any update on database files, Synology Drives sync it to my server, than when I boot up my second PC (or Steam Deck with Windows) Synology Drive sync it to that PC-s database. Like any cloud storage software like Dropbox or Onedrive.
I guess you can make it work for android, if the actual database files are the exact same as for Windows. There is an Android app called Autosync for MEGA, this works with MEGA cloud storage, and previously I successfully synced Retroarch save files with it across Andorid phone and Windows PC, but I have not tried it with Launchbox database files.