is it possible to share my final pro cut purchase to family sharing?

Yes, absolutely.

If you purchase it using your Apple Id, then it will show in the App Store for all the your family members.

All they have to do is select their own account (bottom left), then there is a popup that says "Purchased by". This will let family members get the software purchased by you or other members of the family.

The App Store page says it supports Family Sharing.