It's not clear which parts of Claude state are safe to sync and which you want to keep local to one machine. I'm doing something with syncthing trying to keep agent session history available and little bits of it keep breaking. I haven't looked at this new feature in atuin does it have a really good understanding of what is worth syncing?
One of the Atuin engineers here. Not sure wht your definition of safety is, but Atuin doesn't attempt anything special in terms of deciding what to sync. Pretty much everything is synced.
All your sessions are end-to-end encrypted so only your machines have access to your sessions! Happy to answer any other questions!