Hi,
what size of iCloud storage plan do you have?
iCloud+ plans and pricing - Apple Support
If you have a 256GB phone you would need most likely the 2TB plan, unfortunately there is nothing between 200GB and 2TB.
Please check iCloud as soon as all photos are uploaded!
After all your photos are uploaded to the iCloud you can tell your phone to use photos with reduced resolution on the iPhone.
If you select "Optimize iPhone Storage" your phone will automatically replace the full-size photos with local copies in a lower resolution.
Manage your photo and video storage - Apple Support
iPhone will manage the free space, as soon as it will get full it will replace the photos.
iCloud will have original photos in full resolution / quality
iPhone will have smaller versions of all photos
Attention:
A local backup of your iPhone will then only contain the smaller versions of your photos.
Therefore it would be a good idea to have a backup of your photos in full resolution on a synced MacBook or PC.
Ralf