iPhone storage

iCloud can only help in a limited way with a shortage of storage on an iPhone (with iCloud Photos Optimize storage).

iCloud Backup does not remove any data from the iPhone.

See information in What's the difference between device storage and iCloud storage? - Apple Support (PH)

To turn on iCloud Photos, see the instructions in Set up and use iCloud Photos - Apple Support including the "If you need more device storage" section.

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.

You can’t move all iPhone storage to the iCloud , iPhone storage and iCloud storage are not the same ,, what it’s in iCloud stays there and what it’s in the iPhone like the iOS apps settings it’s in iCloud and all your downloaded apps settings what you can do is free space storage from your the iPhone likeathe texts messages but for a better look go to settings/general/iPhone storage and wait to all info it’s loaded then you can see apps that are using large data info then you can delete what you don’t need