Let's take a look at your log (I have redacted the full paths):
DEBUG |20250304 01:06:07|Loading post-processing engine object (none)
INFO |20250304 01:06:07|Initializing post-processing engine
DEBUG |20250304 01:06:07|1 files to process found
INFO |20250304 01:06:07|Beginning post processing file [REDACTED]/site-[REDACTED]-20250304-020504cet.zip
INFO |20250304 01:06:07|Finished post-processing file [REDACTED]/site-[REDACTED]-20250304-020504cet.zip
DEBUG |20250304 01:06:07|Not removing processed file [REDACTED]/site-[REDACTED]-20250304-020504cet.zip
INFO |20250304 01:06:07|Post-processing has finished for all files
DEBUG |20250304 01:06:07|Akeeba\Engine\Core\Domain\Finalization::_run() Running new finalization object Akeeba\Engine\Core\Domain\Finalizer\UploadKickstart
DEBUG |20250304 01:06:07|Akeeba\Engine\Core\Domain\Finalization::_run() Running new finalization object Akeeba\Engine\Core\Domain\Finalizer\LocalQuotas
DEBUG |20250304 01:06:07|Akeeba\Engine\Core\Domain\Finalization::_run() Running new finalization object Akeeba\Engine\Core\Domain\Finalizer\RemoteQuotas
DEBUG |20250304 01:06:07|No remote quotas were defined; old backup files will be kept intact
DEBUG |20250304 01:06:07|Akeeba\Engine\Core\Domain\Finalization::_run() Running new finalization object Akeeba\Engine\Core\Domain\Finalizer\ObsoleteRecordsQuotas
DEBUG |20250304 01:06:07|Akeeba\Engine\Core\Domain\Finalization::_run() Running new finalization object Akeeba\Engine\Core\Domain\Finalizer\MailAdministrators
As you can see, you have not set any post-processing i.e. you are not telling Akeeba Backup to move the files anywhere. Moreover, we can see that the quota management runs without deleting any files.
You say that you have checked that the backup files do not exist. This means that either you have set up some automation which deletes the backup archives, or the host has set up some automation which deletes the backup archives.
Nicholas K. Dionysopoulos
Lead Developer and Director
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