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Drupal Version 10.0.9
Backup and Migrate Version: 5.0.3
PHP Version 8.0.28

I Could not save backups to private destination.

To solve:
1. Once I was sure that Private Files folder was setup correctly in settings.php as per #56 & #66
2. Error still apparent
3. Uninstalled Backup_Migrate
4. Re-install Backup_Migrate
Saving backup to Private files destination worked first time!

#67 worked for me. Thank you @web226

#67 worked for me too.

I also encountered this issue on a server where the site root was in a symlinked directory.

Even after following the steps above, the problem persisted until I changed settings.php to use the real (non-symlink) path.