Help request to restore lost photos.

Recently returned from holiday, having taken photos on an iPhone 13 mini, photos stopped working as 128 GB storage was full (including 79 GB of System Data). As the Photos settings were set to backup to iCloud, I expected the photos to be saved in iCloud, and on the phone, but to make sure, I took a backup on the phone.

Next, we went to the Apple Store's Genius Bar to get them to reduce the amount of system data, so they set up the iPhone as a new device, having checked that backup to iCloud was enabled. When restoring the iPhone, the option taken was to restore from the iCloud account and not the recent backup. That solved the system data issue; however, the photos from the holiday were not recovered.

A second visit to the Apple Store, they assisted by helping to restore from backup, seeing if this would recover the lost photos, and at the same time accepting that this may also restore the system data issue. Post-restore, the system data issue indeed has returned but did not solve/restore the lost photos.

I suspect the photos on the iPhone had not been synced to iCloud storage, so they were never saved other than on the iPhone, so when the iPhone was set up as a new device, all the holiday photos that were on the phone were lost and lost forever.

Can anyone confirm if my assumption is correct in that there is no way of recovering the holiday photos?

Many thanks.