My family member has more than enough ICloud storage purchased, and she chose to share it with me. How do I utilize that ICloud data on this phone?

Share iCloud+ with your family - Apple Support

"When you share iCloud+, any family members using the free 5GB plan are added to your family plan automatically."

"If a family member is already paying for their own iCloud+ plan, they can choose to switch to your plan or keep their own and still remain part of the family. When they switch to the shared family plan, they get a refund for the remainder of their personal plan. They can't keep their current plan and use the shared family plan at the same time."

Sometimes you need to restart a device, or sign in and out again, in order for it to take a fresh look at sharing status.

You can turn on whatever services you wish to sync at settings > Apple ID > iCloud