Why is the hierarchy type I created not visible in the Manage Hierarchy UI?

When you create a hierarchy type, you must also update the list of hierarchy lookups. You can't use the new hierarchy type, unless you have updated the hierarchy lookup list.

You can update the list of hierarchy types using the Manage Hierarchy Lookups task. Select Party Hierarchy Type (PARTY_HIERARCHY_TYPE) lookup type to edit. Add the new hierarchy type to the Party Hierarchy Type lookup type. After updating the list of hierarchy type lookups and saving your changes, you can view the new hierarchy type under the list of hierarchy types.