Description

When using --backup --backup-dir --delete, rsync was silently removing empty directories from the destination instead of preserving them in --backup-dir. Files in those directories were backed up correctly, but the empty directories themselves were not.

Root cause

delete_item() routed S_ISDIR directly to do_rmdir_at(), bypassing the make_backups/backup_dir logic that only existed in the non-directory else branch.

Fix

After delete_dir_contents() processes all children, delete_item() attempts rmdir() first — this is the atomic emptiness proof. If anything survived inside (e.g. a protect-filtered file), rmdir() fails and the directory is left untouched. If rmdir() succeeds, mkdir() recreates the directory in --backup-dir. EEXIST from mkdir() is expected when child file backups already created the target directory.
Also fixes rmdir() error handling on Solaris, which returns EEXIST (errno 17) instead of ENOTEMPTY for non-empty directories — both are POSIX-valid. The existing check now handles both.

Fixes #842.

Tests added in testsuite/backup-empty-dir_test.py:

• Phase 1: basic --backup does not keep empty directories in --backup-dir #842 reproducer — empty dir appears in backup-dir
• Phase 2: collision safety — existing backup-dir/sub/ from child file
  backups is not destroyed when parent dir is later backed up
• Phase 3: nested empty directories (a/b/c)
• Phase 4: no regression without --backup-dir — empty dir still deleted
• Phase 5: --delete-delay variant — backup path reached for queued deletions