Short answer, out the box they are not mapped.
As long as the id of the attribute is the same, then it will copy over.
out the box in the objects are configured like this:
- IDEA = obj_business_owner
- PROJECT = obj_stakeholder1
One way would be to create another lookup type attribute on the project with id = obj_business_owner
You could also create your own custom attributes for both, this could be useful if your business owners are not users in Clarity. (for example set it up to a custom lookup of the AD)
Alternatively you can build mappings
Convert Clarity Idea into Incident