The iCloud backups are rolling backups, and the most current one will replace the the older backups.
It would not matter anyway, as the iCloud backup of your iPhone does not include the photos at all, if you are have been using iCloud Photos. The iCloud backup only includes items that are not stored in iCloud. You have to archive your iCloud data separately to have a backup of your iCloud data. See: What does iCloud back up?Apple Supporthttps://support.apple.com › en-us
Do you also have a backup you made on a computer? Only the backups on a PC can be archived, so you can have several older backups.
Is your other iPhone a new device? IF you just got yourself a new iPhone, you probably still have access to Apple Care. Contact Apple Support and explain you misunderstood how iCloud Photos is working and that your backup does not include your photos. Perhaps Apple Support can recover your photos for you from Apple's cloud servers. These backups are not accessible for the users, but perhaps Apple will oblige and help a good customer in such an emergency.
Unfortunately, this is a very common mistake when setting up a new iPhone.