How do I recover my photos from my old cloud account?

You need to sign into your old iCloud account to recover the photos. On a computer, sign into System Preferences/iCloud (Apple ID for Catalina or later) using the old ID, and turn Photos syncing on. On a device, sign into Settings/Your Name/iCloud and turn Photos syncing on. Or go to iCloud.com/Photos using a computer browser and download the photos from there.