Once you sync your Lightroom Classic Catalog file with your Creative Cloud storage it will sync all the original files that have been synced by Lightroom (cloud-based) desktop app and Lightroom mobile devices connected with your Adobe ac.
Classic must have original image files, locally connected to your computer. There are two Lightroom applications that can function on your computer. See the screen capture.
LrC functions with the original files connected to your local system. You can sync Collections from LrC to the cloud it will sync smart previews will be available to your mobile devices.
Lr - desktop app. syncs original files to your Cloud storage, which will connect yith all your mobile devices.
Make little sense having LrC and Lr on the same computer.
Regards, Denis: System iMac mid-2015, 5K 27” monitor, macOS10.15.7: LrC 10, Lr 4, Ps 22.0,; Camera OM-D E-M1.
I'm sorry, but that is not how the ecosystem works. There is no option for selective sync from the cloud to Lightroom Classic, only vice versa. Lightroom Classic will download all the cloud images if you enable sync.