Not enough Storage on MAC
My MAC told me that there is not enough space to load more photos. I deleted all photos from my MAC because they were stored in ICloud. Now they are not in Icloud either. Can these be recovered?
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Recover them from Recently Deleted. Click Recently Deleted in the Photos sidebar on your Mac, then select the photos and click Recover. Also see: If you're missing photos or videos in the Photos app - Apple Support
As you have found, iCloud Photos is a syncing service. Any photo you delete from a device where iCloud Photos is turned on will also be deleted from iCloud and from any other device connected to iCloud Photos. You can potentially reduce the storage space required on a device by turning on Optimize Storage. See: Set up and use iCloud Photos - Apple Support
Apple does not currently offer cloud-only storage for photos. If that is what you want or need, you may want to explore 3rd party options such as Google Photos or Dropbox.