Assuming only one "best practice" is a trap. There always is more than one solution.
Storing the contents of the config files in the database is one option. Blobs managed by some application, possibly written out to disk if that is what some other thing is reading. Or alter the application to use discrete data fields in the DB rather than YAML documents. Takes advantage of the existing central database, but requires that DB to be available first.
Store the config files in the software package or image containing the application. Deploy new ones by upgrading the app. Only makes sense if those files are changed by the same people or process updating the application.
Copy the files from the authoritative copy to each instance on a schedule, or on change. Take your pick of file copy software, rsync, sftp. Would need some extra scripting if the install should be transactional, in that all of the files are installed, or none of them are.
Mount a network file share. Beware that if NFS or SMB shares are disconnected in an unplanned manner, that can cause performance issues.