@forteller The simplest option is a sync app connected via SFTP or SMB, a quick search in F-Droid shows 'Round Sync' as a potential option. Nothing to install on your PC this way.
The other option is Immich, it's more of a full photo management server you would install on your PC or a local always-on server, but the mobile app has auto-backup that works really well, and it gives you more functions like albums, face recognition, search, etc..
I do not recommend Syncthing as it cannot easily do one-way sync while also not syncing deletions, which is typically how people want photo sync/backup to function. And the mobile app doesn't often work well and can cause high battery drain in my experience.
@delegatevoid It's a pretty big learning curve, as it works in a very different way from Lightroom, and the 'flow' I find very confusing.
But it can replace most of Lightroom.
@jamesthebard NFS is just horrible in general, I've never had good luck with it, always performance or other odd issues.
For copying docker volumes they are in /var/lib/docker/volumes by default and you can tar that whole directory and copy to the new host.