How do I free up photo storage space on my phone if I have everything on iCloud?

You can't keep them only on iCloud but you can turn on the Optimize iPhone Storage option.

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.

Here is some information that should help you manage your storage.

iDevice:

How to check the storage on your iPhone, iPad, and iPod touch  https://support.apple.com/en-us/HT201656

How to free up space on an iPhone https://www.macworld.co.uk/how-to/iphone/free-space-iphone-3524712/

10 Easy Ways To Free Up A Lot Of Space On Your iPhone https://www.huffpost.com/entry/iphone-free-space-tips_n_6269756

iPhone Other storage: What is it and how do you delete it?

https://www.macworld.com/article/3388219/iphone-other-storage-what-is-it-and-how-do-you-delete-it.html 

iCloud:

Check your iCloud storage usage on iCloud.com https://support.apple.com/guide/icloud/check-your-storage-usage-mm6e5a441fc7/1.0/icloud/1.0

Manage your iCloud storage https://support.apple.com/en-us/HT204247