Sep 18 04:30:35 osmc mediacenter[1214]: cp: cannot create regular file '/mnt/backup/OSMCBACKUP_2023_09_18_04_29_22.tar.gz': Permission denied
2023-09-18 08:52:15.380 T:1419 debug <general>: script.module.osmcsetting.updates[osmc_backups] : local tarball name: /home/osmc/.kodi/temp/OSMCBACKUP_2023_09_18_08_51_14.tar.gz
2023-09-18 08:52:15.380 T:1419 debug <general>: script.module.osmcsetting.updates[osmc_backups] : local tarball exists: True
2023-09-18 08:52:15.380 T:1419 debug <general>: script.module.osmcsetting.updates[osmc_backups] : remote tarball name: /mnt/backup/OSMCBACKUP_2023_09_18_08_51_14.tar.gz
2023-09-18 08:52:15.381 T:1419 debug <general>: script.module.osmcsetting.updates[osmc_backups] : remote tarball exists: False
2023-09-18 08:52:15.712 T:1419 debug <general>: script.module.osmcsetting.updates[osmc_backups] : Transfer of backup file not successful: False
It looks like you have a permissions issue to where your trying to create the backup. I would suggest to look over the following post and tweak your mount point…