Unified backups: Refactor database target for backups

The following discussion from !166612 (merged) should be addressed:

@brodock started a discussion: (+4 comments)

                pipeline_status = pipeline.run!(input: db_file_name, output: decompress_wr)

                decompress_wr.close

                status, tracked_errors =
                  case config[:adapter]
                  when "postgresql"
                    Gitlab::Backup::Cli::Output.print_info "Restoring PostgreSQL database #{database} ... "
                    execute_and_track_errors(pg_restore_cmd(database), decompress_rd)
                  end
                decompress_rd.close

                $CHILD_STATUS.success? && status.success? && pipeline_status.success?