iCloud Backup: Photos without iCloud Photos?

When iCkoud Photos is enabled, iCloud backups do not include photos.

When iCkoud Photos is disabled, and you are making iCloud backups, there is a separate switch that determines if those backups include photos.

Note that if you are not backing up photos in any way, you can easily lose them all if you forget your passcode or if something happens to your phone.

"iCloud Backup: Photos without iCloud Photos?"

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Backing Up your iCloud Drive Elsewhere:

"I have a question regarding backing up an iPhone before transferring data to a new iPhone. I would like to do so through iCloud (I don't have access to a computer with enough space in the short term)"

You can export all of iCloud to an external source, such as a hard drive. See my User Tip for this: Getting a Quick and Direct "iCloud Drive-to-External Hard Drive" Download - User Tip

iCloud Photos Uploading to iCloud If Not On:

"The apple help pages are unclear as to whether an iCloud backup will save photos if iCloud photo saving is NOT turned on (and to reiterate, I don't want it turned on). Will it turn iCloud photos on?? Will it store the photos separately? Will it simply not store them?"

No. They will not upload, if you've selected not to; they will stay locally stored.