iCloud Photos is not a backup service. It is designed to sync your photos on all your devices. For more info, see:
Get help with iCloud Photos - Apple Support
When you turn on iCloud Photos, all of your photos and videos are securely stored in iCloud. So they are no longer included in your iCloud backup. However, if you delete a photo on any device it is deleted on all your devices (including iCloud).
If you have Optimize Storage turned on, you might not have all of your original photos and videos on your device. To download the original photos and videos on your iOS device, go to Settings > [your name] > iCloud > Photos and select Download and Keep Originals. See the 'Store your photos and videos in iCloud' section in:
Manage your photo and video storage - Apple Support
"With Optimize Storage, smaller, space-saving photos and videos are kept on your device while all of your original, full-resolution versions are stored in iCloud. And as long as you have enough space in iCloud, you can store as many photos and videos as you want."
From what you describe, you do not want to use the Optimize storage setting or even use iCloud Photos at all. Instead simply turn off Optimize storage and iCloud Photos and include the photos as part of your normal Cloud backup. For more info, see:
What does iCloud back up? - Apple Support
and the 'Manage your iCloud Backup' section in:
Manage your iCloud storage - Apple Support
