After a thorough review of logs on both the NAS and HA Supervisor, I believe I have found the reason for this issue. I am using a Google Drive Backup add-on, and while I ran the HA on the RPi5, in order to save space, I’ve had the option to remove backups from the local system after uploading them to Google Drive. I did not turn this feature off after moving the HA to a virtual machine on the NAS. In the HA Supervisor logs, I could see that it is the Google Drive Backup that accesses the file at the same time, 04.00.39, as the time of file removal on the NAS.
It appears that the Google Drive Backup add-on utilizes the same directory as Home Assistant’s system backups. When the option to delete local backups after uploading to Google Drive is enabled, the add-on removes all files within that directory—regardless of their origin—potentially including unrelated or manually created backups.