An error occurred while loading a higher-quality video on iPhone

Your iPhone may not have enough space to store all high-resolution photos and videos from iCloud.

Please compare 

Settings>your name>iCloud>Manage Storage

And

Settings>General>iPhone Storage

This will give you a fair idea of how to manage your device and iCloud storage.

Some of the links below may help

1. Manage iCloud Photos iCloud Photo Library Help - Apple Support 
2. Manage your iPhone Storage --> Manage your photo and video storage - Apple Support
3. Manage your iCloud Storage → Manage your iCloud storage - Apple Support