The 'Adobe Creative Cloud' is not the place to 'save' images. In fact this service will end in Feb 2024-
https://community.adobe.com/t5/lightroom-classic-discussions/p-does-the-deprecation-of-synced-creative-cloud-files-on-feb-1-2024-affect-lightroom-syncs/td-p/13977917
Lightroom (when online) will automatically 'save' your edits to the Lightroom ecosystem where the Lightroom-mobile apps will see your edits synced across devices.
So any editing done in Lightroom-Desktop v6.5 (PC or Mac), Lightroom-mobile (iPhone, iPad, Android), or Lightroom-Web (Browser), will sync across all devices (for the one account).