I have spare storage in my phone but no storage in my icloud

You can do that and you can turn off iCloud Photo Sync. Simply said, iCloud is not an archive. It is a syncing service. If you have iCloud Photo Sync turned on, when you delete a photo on your phone, it will delete from the cloud.

If you just want to keep your photos on your computer and not in iCloud, this link will explain how to do that --> Download iCloud photos and videos - Apple Support

Once your photos are safely stored to your computer, on your phone you can then go to Settings > Your Name > Apple ID, iCloud, iTunes & App Store. Then tap iCloud. Then turn off photos. Your photos will stay on your phone and no longer sync to iCloud.

The physical space on your phone and the amount of iCloud storage are different. You got 5GB free with your Apple account. If you need more, it's time to buy more space.

This link will tell you how you can do that --> Upgrade your iCloud storage plan - Apple Support