Terminology conflict I think :-) The pg_rman docs call backup retention management "backup maintenance" , and retention management is one of the things on the barman todo list.
As for compression, I think barman does log compression not the backups, but it could simply be that the barman docs [1] are out of date where they say :
"Barman’s most wanted features include: backup catalogues, retention policies, remote recovery, archiving and compression of WAL files and of backups."