I want to delete photos from my iPhone to free up memory

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 the following Apple article for more information: 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.

Another way that photos may be on iCloud (if you don’t have iCloud Photos turned on) is via a backup of an iOS device. The only thing you can do with a backup is use it to restore a device or set up a new device. The contents of backups are not viewable at iCloud.com and if you delete a photo from a device it will not be included in future backups and will be lost.

You could use a Mac running Photos to Export photos from the Photos library to some place outside of the system Photos Library, and to back up the exported copies.

Once you did that, you could delete the photos from iCloud Photos. Photos that you offloaded in this way would no longer be visible in Photos on your iPhone, even if one of the places to which you copied them was iCloud Drive.

Note that Macs can have multiple Photos libraries. Hold down the Option key, while launching Photos, to get the dialog that lets you create and switch between libraries.

At most one of the Photos libraries (the system Photos library) can synchronize with iCloud. The others will just be for local storage. Also, Apple does not provide any tools for working with multiple libraries at the same time. So it is more difficult to compare the contents of libraries, and to move photos between them, than it needs to be.