Deleting photos on iCloud to regain storage

If you have iCloud Photos turned on to sync your iPhone photos with iCloud, the resolution of the photos on your phone doesn't change unless you have the Optimize iPhone Storage option turned on and your phone is low on storage space. See the following from Set up and use iCloud Photos - Apple Support

If you need more device storage

iCloud Photos keeps all your photos and videos in their original, high-resolution version. To save storage space on your device, you can turn on Optimize Storage.

If you turn on Optimize Storage, iCloud Photos automatically manages the size of your library on your device. Your original photos and videos are stored in iCloud and space-saving versions are kept on your device. Your library is optimized only when you need space, starting with the photos and videos you access least. You can download the original photos and videos over Wi-Fi or cellular when you need them.

If you turn on Download Originals, iCloud Photos keeps your original, full-resolution photos and videos in iCloud and on your device.

Also be aware that 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.

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.

Sorry, I don't know about the circumstances or accuracy of that email.

Also, re your statement "...deleted the auto sync of my photos as well as the existing photos in iCloud as I wanted to free up my storage for regular iPhone backups"

Be aware that when you had iCloud Photos turned on, your photos were not also included in iCloud Backup. Now that it is turned off, your photos will be included in iCloud Backup unless you specifically excluded them. You won't have freed up any space.