There is a scenario in which i add something inside the pg_tablespace directory , i am getting an error like-
pg_validatebackup: * manifest_checksum = 77ddacb4e7e02e2b880792a19a3adf09266dd88553dd15cfd0c22caee7d9cc04 pg_validatebackup: error: "pg_tblspc/16385/PG_13_202002271/test" is present on disk but not in the manifest
but if i remove 'PG_13_202002271 ' directory then there is no error
This seems expected considering current design as we don't log the directory entries in backup_manifest. In your case, you have tablespace with no objects (empty tablespace) then backup_manifest does not have any entry for this hence when you remove this tablespace directory, validator could not detect it.
We can either document it or add the entry for directories in the manifest. Robert may have a better idea on this.