The default directory /var/lib/barman don't has the server directorys if you make a backup without previously doing a barman check SERVER command, this would create it.
Maybe it's a bad idea to start backup without doing check, but somehow it should look for the needed directorys. If it is not there you are getting this in postgres log
rsync: change_dir#3 "/var/lib/barman/SERVER/incoming" failed: No such file or directory (2)
rsync error: errors selecting input/output files, dirs (code 3) at main.c(633) [Receiver=3.0.7]
rsync: connection unexpectedly closed (9 bytes received so far) [sender]