What kind of backup did you make of your iPhone?
The iCloud backup of an iPhone does not include the photos that are in iCloud, so it'd does not give any added security for our photos. So you must not delete any photos from iCloud on any of your devices while the device is still syncing with iCloud Photos, because you have no backup of the iCloud Photos and any photo you delete from your old iPhone will be deleted from iCloud and your new iPhone as well. We need to make regular backups of our iCloud Photos on a computer to keep them safe, or have to be very, very careful, when deleting redundant photos, for it is very easy to delete accidentally more photos than we want to delete. On the tiny iPhone display we cannot see all selected photos.