There is a related feature request. Obsidian Sync: Sharing a vault
Obsidian works on files. So you could use any third party file sharing service.
I assume that most Business oriented file sharing systems offer file or directory level access control.
However it seems that what you want goes way beyond this.
It seems that you want content-level permission. I am not sure such a system even exists. How would any sync service know what to sync not to sync based on content? The system should read your file, use some sort of AI to determine if it’s sensitive or not, and then share it accordingly?