I have made a test with PostgreSQL client 10 on CentOS 7:
# yum info postgresql10
Loaded plugins: fastestmirror
Loading mirror speeds from cached hostfile
* base: centos.mirrors.proxad.net
* centos-sclo-rh: centos.mirror.fr.planethoster.net
* centos-sclo-sclo: centos.mirrors.proxad.net
* extras: centos.mirrors.proxad.net
* updates: centos.mirrors.proxad.net
Installed Packages
Name : postgresql10
Arch : x86_64
Version : 10.12
Release : 1PGDG.rhel7
Size : 8.3 M
Repo : installed
From repo : pgdg10
Summary : PostgreSQL client programs and libraries
URL : https://www.postgresql.org/
License : PostgreSQL
Description : PostgreSQL is an advanced Object-Relational database management system (DBMS).
: The base postgresql package contains the client programs that you'll need to
: access a PostgreSQL DBMS server, as well as HTML documentation for the whole
: system. These client programs can be located on the same machine as the
: PostgreSQL server, or on a remote machine that accesses a PostgreSQL server
: over a network connection. The PostgreSQL server can be found in the
: postgresql10-server sub-package.
:
: If you want to manipulate a PostgreSQL database on a local or remote PostgreSQL
: server, you need this package. You also need to install this package
: if you're installing the postgresql10-server package.
It has following executables
# ls -rtl /usr/pgsql-10/bin
total 2372
-rwxr-xr-x 1 root root 581984 11 févr 23:04 psql
-rwxr-xr-x 1 root root 126152 11 févr 23:04 pgbench
-rwxr-xr-x 1 root root 79576 11 févr 23:04 pg_waldump
-rwxr-xr-x 1 root root 125752 11 févr 23:04 pg_upgrade
-rwxr-xr-x 1 root root 24784 11 févr 23:04 pg_test_timing
-rwxr-xr-x 1 root root 29104 11 févr 23:04 pg_test_fsync
-rwxr-xr-x 1 root root 79744 11 févr 23:04 pg_rewind
-rwxr-xr-x 1 root root 159544 11 févr 23:04 pg_restore
-rwxr-xr-x 1 root root 67568 11 févr 23:04 pg_receivewal
-rwxr-xr-x 1 root root 92616 11 févr 23:04 pg_dumpall
-rwxr-xr-x 1 root root 384352 11 févr 23:04 pg_dump
-rwxr-xr-x 1 root root 28752 11 févr 23:04 pg_config
-rwxr-xr-x 1 root root 105488 11 févr 23:04 pg_basebackup
-rwxr-xr-x 1 root root 28816 11 févr 23:04 pg_archivecleanup
-rwxr-xr-x 1 root root 54488 11 févr 23:04 dropuser
-rwxr-xr-x 1 root root 54520 11 févr 23:04 dropdb
-rwxr-xr-x 1 root root 59272 11 févr 23:04 createuser
-rwxr-xr-x 1 root root 58840 11 févr 23:04 createdb
-rwxr-xr-x 1 root root 63256 11 févr 23:04 vacuumdb
-rwxr-xr-x 1 root root 58960 11 févr 23:04 reindexdb
-rwxr-xr-x 1 root root 54448 11 févr 23:04 pg_isready
-rwxr-xr-x 1 root root 58872 11 févr 23:04 clusterdb
#
This means it should be possible to install only PostgreSQL client for barman.
apt
on Ubuntu 18.04 (and I assume others), installing barman automatically installs those two binaries as dependencies without installing the server.