How did you back up the photos to iCloud? Did you sync your old Mac with iCloud Photos or did you copy the Photos Library to iCloud Drive?
If you have used iCloud Photos and your photos are in iCloud, you should simply enable iCloud Photos in Photos on your Mac and wait for the photos to come back from iCloud - as described here: If you're missing photos or videos in the Photos app - Apple Support (IN) (in the second part of the article - scroll down to "Make sure iCloud Photos is turned on" .
If your photos really have been synced to iCloud Photos you should be seeing them on your iCloud web page at www.icloud.com , when you open the Photos.app on that page.
You wrote "The information says I need to use an older OS". if you are getting a warning about needing to use an older version of macOS, you may be trying to run an old version of Photos. Perhaps you have restored the old Photos.app from your backup drive instead of the Photos Library. the old version of Photos can only run on a Mac with an older system version.
Or you have saved an old iPhoto Library instead of your Photos Library. A new Mac with macOS Sonoma or Ventura can no longer open iPhoto Libraries.
What is the exact error message you are getting, literally?